Questions on Word Problems: Miscellaneous Word Problems answered by real tutors!

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Question 571229: if it takes 4 hours for a group of people to paint a house and 6 hours for another group of people to paint another house, How long will it take for both groups of people to paint a house together?
Answer by nerdybill(5403)

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if it takes 4 hours for a group of people to paint a house and 6 hours for another group of people to paint another house, How long will it take for both groups of people to paint a house together?
Let x = time (hours) it takes for both groups
then
x(1/4 + 1/6) = 1
multiply both sides by 12:
x(3 + 2) = 12
x(5) = 12
x = 12/5
x = 2.4 hours

Question 571204: Rebekah's recipe for 4 1/2 dozen cookies calls for 6 cups of sugar. How many cups of sugar are needed to make 8 dozen cookies?

9 2/3 cups

12 2/3 cups

11 2/3 cups

10 2/3 cups

Answer by mrjunecarlo1095@ymail.com(6)

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10 2/3 by RATIO AND PROPORTION

Question 571031: Find two numbers whose sum is 54 and whose product is 665.
Answer by nyc_function(2626)

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We have two equations in two unknowns.

a + b = 54

a*b = 665

======================================

Solving a + b = 54 for a, I get a = 54 - b.

I then plug 54 - b in the equation a*b = 665.

(54 - b)*b = 665

I proceed to solve (54 - b)*b = 665 for b.
Solving for b, I get two answers: b = 19 and b = 35.
To find a, I must replace either original equation with either value of b.
I will use b = 19.

a + b = 54

a + 19 = 54
a = 54 - 19

a = 35.

The numbers are 19 and 35.

Question 570898: Hope went shopping and found a pair of jeans that had been marked down four times. The purchase price was a combination of the mark downs. The jeans started at $49.99. The first mark down was 20%, that price was marked down 30%, the third mark down was 10%, and the final mark down was an additional 20%. How much were the jeans?
Answer by josmiceli(6769)

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Let +p+

= the original price
The 1st markdown makes the price
+p+-+.2p+=+.8p+

The 2nd markdown makes it
+.8p+-+.3%2A.8p+=+.8p%2A%28+1+-+.3+%29+

The 3rd markdown makes it
+.56p+-+.1%2A.56p+

The 4th markdown makes it
+.504p+-+.2%2A.504p+

given:

Hope bought the jeans for $20.16

Question 570899: Shalisha buys a 32-pound pumpkin and pays $12.48 for it. How much does the pumpkin cost per pound?
Answer by nerdybill(5403)

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12.48/32
0.39
that's 39 cents per pound

Question 570856: Gabe, a Nuclear Physicist, needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 liters of 50% acid solution?
Answer by josmiceli(6769)

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Let +a+

= liters of 30% solution needed
Let +b+

= liters of 60% solution needed
given:
(1) +a+%2B+b+=+90+

(2)

----------
(2) +.3a+%2B+.6b+=+.5%2A90+

(2)

(2)

Multiply both sides of (1) by +3+

and subtract (1) from (2)
(2) +3a+%2B+6b+=+450+

(1)

and, since
(1) +a+%2B+b+=+90+

(1)

(1)

30 liters of 30% solution are needed
60 liters of 60% solution are needed
check:
(2) +%28+.3a+%2B+.6b+%29+%2F+90+=+.5+

(2)

+%28+.3%2A30+%2B+.6%2A60+%29+%2F+90+=+.5+

(2)

(2)

(2)

Question 570387: I am not sure if this under the right category but here is the question..
The Mars Rover Spirit landed on Jan 3, 2004. Just over one year later on Jan 14 2005 the huygens probe landed on Titan. At the closest approach the distance from Earth to Saturn is 29 million miles more than 21 times the distance from Earth to mars. If the distance to Saturn is 743 million miles, what is the distance to mars?
Answer by Edwin McCravy(6929)

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All we need are these words:

the distance from Earth to Saturn is 29 million miles more than 21 times the distance from Earth to mars. If the distance to Saturn is 743 million miles, what is the distance to mars

Let x = the distance from Earth to Mars (in millions of miles)

the distance from Earth to Saturn is 29 million miles more than 21 times the distance from Earth to mars.

Replace the words "the distance from Earth to Saturn" by 743

743 is 29 million miles more than 21 times the distance from Earth to mars.

Replace the words "the distance from Earth to Mars" by x

743 is 29 million miles more than 21 times x.

Replace the words "21 times x" by 21x

743 is 29 million miles more than 21x.

Erase the "million miles", because that's understood

743 is 29 more than 21x.

Replace the words "29 more than 21x" with 21x + 29

743 is 21x + 29

Replace the word "is" by an equal sign "=":

743 = 21x + 29

Subtract 29 from both sides:

714 = 21x

Divide both sides by 21

34 = x



Answer: It's 34 million miles from Earth to Mars.    



Edwin

Question 570236: if the length of one side of a square is doubled and the length of an adjacent side is decreased by 3, the area of the resulting rectangle exceeds the area of the original square by 16. The length of a side of the original square is?
Answer by ankor@dixie-net.com(12681)

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if the length of one side of a square is doubled and the length of an adjacent side is decreased by 3,
the area of the resulting rectangle exceeds the area of the original square by 16.
The length of a side of the original square is?
:
Let s = length of the side of the original square
then
s^2 = original area
:
and the new rectangle dimensions will be
2s by (s-3)
:
New area - old area = 16
2s(s-3) - s^2 = 16
2s^2 - 6s - s^2 = 16
2s^2 - s^2 - 6s - 16 = 0
s^2 - 6s - 16 = 0
Factors to
(s-8)(s+2) = 0
positive solution
s = 8 units, the length of the original square
:
:
Check this by finding the areas
16(8-3) = 80
8*8 = 64
-------------
differ; 16

Question 570234: The sum of the digits of a two-digit number is 6. When the digits are reversed, the new number is 36 more than the original number. Find the number.

Answer by Maths68(1140)

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Let
x and y are two digits of a number
number = n

Sum of the digits
x+y=6.....................(1)
When x is ten and y is unit
10x+y=n.............(2)
When the digits are reversed, the new number is 36 more than the original number
Now y is ten and x is unit
10y+x=n+36.............(3)
Subtract (2) from (3)
10y+x=n+36.............(3)
-10x-y=-n.............(2)
-------------------------
-9x+9y=36
9(y-x)=36
9(y-x)/9=36/9
y-x=4...................(4)
Add (1) and (4)
y-x=4...................(4)
x+y=6.....................(1)
-----------------------------
2y=10
2y/2=10/2
y=5
Put the value of y in (1)
x+5=6.....................(1)
x=6-5
x=1
Number = 15
When the digits are reversed = 51 (15+36=51)

Question 570188: eleven more than twice the number is 19, find the number.
Answer by JBarnum(1826)

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11+2n=19
2n=8
n=4

Question 570172: Find the measure of two complementary angles if one angle is 9 deg more than two times the other angle.
Answer by JBarnum(1826)

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angle (a) and angle (b)
a=9+2b
a+b=90
9+2b+b=90
3b=81
b=27
90-27=63
a=63

Question 569568: All of M. Newsome's books were published in volumes exactly 5 in. wide and 8 in. high. How many of his volumes could be put in a sqauare that is 45 in. wide and 48in. high?
Answer by KMST(576)

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I guess you have a rectangular end table, 45 inches by 48 inches (It’s not a square if the sides’ lengths are different).
You can place books side by side with the 5 inch book side with along the 45 inch rectangle side until you have a row of 9 books
covering (with a row 8 inches high) the 45 inch width:
9%2A5

inches =

inches
You add rows like that, one after the other and after a total of 6 rows, the whole 48 inch are covered: 6(8”)=48”
6%2A8

inches =

inches
The layer of books covering the 45 inches by 48 inches space would look like this:

drawing%28300%2C300%2C-1%2C54%2C-4%2C51%2C%0D%0Arectangle%280%2C0%2C45%2C48%29%2C%0D%0Aline%285%2C0%2C5%2C48%29%2C+line%2810%2C0%2C10%2C48%29%2C+line%2815%2C0%2C15%2C48%29%2C+line%2820%2C0%2C20%2C48%29%2C%0D%0Aline%2825%2C0%2C25%2C48%29%2C+line%2830%2C0%2C30%2C48%29%2C+line%2835%2C0%2C35%2C48%29%2C+line%2840%2C0%2C40%2C48%29%2C%0D%0Aline%280%2C8%2C45%2C8%29%2C+line%280%2C16%2C45%2C16%29%2C+line%280%2C24%2C45%2C24%29%2C+line%280%2C32%2C45%2C32%29%2C+line%280%2C40%2C45%2C40%29%2C+locate%2818%2C0%2C%2745+inches%27%29%2C+locate%2845%2C25%2C48%29%2C+locate%2845%2C23%2C%27inches%27%29%2Carrow%2847%2C25%2C47%2C48%29%2Carrow%2847%2C20%2C47%2C0%29%2C%0D%0Aarrow%2818%2C-1.5%2C0%2C-1.5%29%2Carrow%2830%2C-1.5%2C45%2C-1.5%29%29

You placed a total of 9(6)=54 books on the table, 6 rows of 9.

Question 570006: using 0,1,2,3,5,6 only once each, find the starting and ending time of a test if it takes 3 hours and 45 minutes
Answer by AnlytcPhil(1116)

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Let the test begin at A:BC and end at D:EF

1. The 45 minutes tell us that C and F differ by 5. 
2. D is 3 more than A, and EF is 45 more than B, or else D is 4 more than A,
   and EF is 15 less than BC.

If D is 3 more than A, then A=2, and D=5, for they are the only ones of the
given numbers which differ by 3.  So F=1 and C=6, or F=6 and C=1.  So the first
case that might seem possible is for the test to begin at 2:01, but that would
make the test end at 5:46, but we can't use 4.  The next seemingly possible
starting time would be 2:06, but that would make the test end at 5:51, which is
out because that uses 5 twice.  Any later starting time would likewise cause 5
to be used twice.  So D is not 3 more than A.

So that means D is 4 more than A, and EF is 15 less than BC. 

So either A=1 and D=5 or A=2 and D=6

If A=1 and D=5 then none of the other given numbers differ by 5, but C&F must
differ by 5.

Therefore A=2 and D=6, and the only 2 left which differ by 5 are 0 and 5, so
either C=5&F=0 or C=0&F=5

Since EF is 15 less than BC, the starting time must be 2:15 or later.  It can't
start at 2:15, for it would end at 6:00 which uses two 0's. It can't start at
2:20 or 2:25, for they use two 2's. If it started at 2:30 it would end at 6:15.

Hey, that is the answer!

But could there be more than one possibility?  Let's see:

It can't start at 2:35 for it would end at 6:20 and that uses 2 twice. There is
no 4, so it can't start at 2:40 or 2:45.  It can't start at 2:50 or 2:55
because C or F must be 5, so B can't be 5.

So we have ruled out every possibility except one:

The test starts at 2:30 and ends at 6:15.

Edwin

Question 570011: 1. Freedom or Alligators
Once upon a time, a prison warden was responsible for 22 prisoners on Death Row. These prisoners were students who had done terrible things: some illegally downloaded movies and music, some texted during classes, some were addicted to Facebook, and some watched Glee.
One day, the warden offers the prisoners one chance at freedom. After a brief discussion period in which they could plan their strategy, each of the prisoners will be placed in solitary confinement (in completely soundproof cells) with absolutely no way to communicate with one another. The warden will arbitrarily take one prisoner at a time to another room containing two light switches side by side. The switches are not connected to anything, but the warden tells the prisoners that at the beginning of the entire process both switches will begin in the “Off” or “Down” position. The rules are that each time one of the prisoners enters the room he or she must flip exactly one of the switches.
The warden tells the prisoners that if one of them ever correctly announces that all 22 prisoners have been in the room that they will all be released. However, if any of the prisoners ever incorrectly claims that all 22 have been in the room, then all 22 will be fed to the warden’s pet alligators.
The warden makes it clear to that prisoners may be returned to the room any number of times, but there is no way for the prisoners to communicate with one another other than by way of the two light switches. The room with the switches will be thoroughly cleaned after each prisoner leaves.
The prisoners are given some time to come up with a plan before they are to be placed in solitary confinement.
How do they ensure their freedom?

Answer by solver91311(12117)

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The prisoners need to choose a leader, who we will hereafter call the "Scorekeeper" The other prisoners will be refered to as "Transmitters"

Designate one of the switches as A and the other as B, i.e. decide that the left hand switch will be A. And then make sure everyone knows their left from their right -- they are students after all.

When a Transmitter enters the room, s/he will take one of the following actions:

If switch B is OFF and this person has never encountered switch B in the OFF position before, turn switch B ON.

If switch B is ON, change the position of switch A.

If switch B is OFF but this person has seen switch B in the OFF position on a previous visit, change the position of switch A.

The Transmitters' job is to wait for that one occasion when they encounter switch B in the OFF position for the first time so that they can turn it on.

When the Scorekeeper enters the room s/he takes one of the following actions:

If switch B is ON, s/he turns it off and adds 1 to the score.

If switch B is OFF, s/he changes the position of switch A and does NOT add to the score.

When the score reaches 21, the Scorekeeper announces that all of the prisoners have visited the room at least once.

I hope the warden takes the students who were convicted of watching Glee and throws them to the alligators anyway.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

Question 569729: what 2 numbers add up to -126 but multiply to get 9720
Found 2 solutions by JBarnum, Alan3354:
Answer by JBarnum(1826)   (Show Source):
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there arent any 2 numbers that work
highest possible to add to -126
-63+-63=-126 and -63*-63=3969
they have to be both negative numbers to make the positive number.
if you know imagenary numbers theres an answer, but you didnt clarify imagenary numbers

Answer by Alan3354(21550)   (Show Source):
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what 2 numbers add up to -126 but multiply to get 9720
----------
x + y = -126 --> y = -126 - x
x*y = 9720
-------
x*(-126 - x) = 9720

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -23004 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -23004 is + or - .

The solution is , or
Here's your graph:

==============================
No real number solution.
The complex numbers shown fit.

Question 569580: Emma is making a model of a Mardi Gras float. She is making it from a shoebox that measures 10 in. wide x 6in. long x 5in. high. She will cover the bottom and all four sides with velvet. How many square in. of velvet will she need?
Answer by JBarnum(1826)   (Show Source):
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this is a perimeter problem minus 1 top side, total(t) square inches
the top and bottom are l*w
the two long sides are h*l
the two short sides are h*w

since theres only the bottom we dont multiply by 2 for the lw sides

Question 569569: James derew a rectangle that was 10in. wide and 14 in. long. Inside the rectangle he drew a triangle. What is the area of the largest triangle he could draw inside the rectangle?
Answer by JBarnum(1826)   (Show Source):
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uh the largest triangle would be exactly half of the area of the rectangle by drawing the diagnal creating 2 90 degree triangles
fastest way is find area of rectangle and divide by 2
140/2=70

Question 569466: A rectangular tank with a base 4 feet by 5 feet and a height of 4 feet is full of water. The water weighs 62.4 pounds per cubic foot. How much work is done in pumping water out over the top edge in order to empty (a) half of the tank? (b) all of the tank?
a)2496 ft-lbs
b)9984 ft-lbs
Explain why the answer in part b is not exactly twice the answer in part a.
I figured out the amount of work (answers above), but I do not know how to explain the answers.
Answer by ankor@dixie-net.com(12681)   (Show Source):
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I am going to guess that it is because, when you pump out the lower half of the tank, (which you would have to do to empty the tank), you have to pump it higher than when you pump out the top half.

Question 569341: 1.)the sum of 2 numbers is 48 and their difference is 24. what are the numbers
2.)a group of students visted an art muesuem . 2 adults and 5 students in one van paid $77. 2 adults and 7 students in the second van paid $95. find the price for 1 adult and 1 student.
3.)the addmission fee at a small fair is $1.50 and $4.00 for adults. on a certain day 2200 people entere the fair and $5050 is collected. how namy children and how namy adults attended
4.)a landscaping company placed 2 orders with a nursery. the first order was for 13 bushes and 4 trees, and tottaled $487. the second order was for 6 bushes and 2 trees and totalled $232. the bills do not list the per item pirce. what were the cost of 1 bush and 1 tree
on all of them you have to define the variables,write yout sytems of equations, and show your work
Answer by solver91311(12117)   (Show Source):
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The first and most important lesson to learn in any field of endeavor, and most particularly in the study of mathematics, is the ability to read and follow instructions. Go back to the page where you posted your questions and re-read (or read for the first time as the case may be) the rather clearly couched instruction that says you may only ask one question per post. Write back when you have read it a sufficient number of times such that you fully comprehend the concept.

John

My calculator said it, I believe it, that settles it

Question 568975: 3. A wire 100 inches long is bent into a rectangle. If the width is
x,
3. How is length represented? What is the function for area?
4. What must be the dimensions of the rectangle so that area is a
maximum?
5. What is the maximum area possible?
Answer by htmentor(580)   (Show Source):
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3. A wire 100 inches long is bent into a rectangle. If the width is
x,
3. How is length represented? What is the function for area?
4. What must be the dimensions of the rectangle so that area is a
maximum?
5. What is the maximum area possible?
==========================================
The perimeter P = 2(l+x) = 100
So l+x = 50 -> l = 50-x
The area, A = l*x = x(50-x) = 50x - x^2
To maximize the area, set dA/dx = 0:
dA/dx = 50 - 2x = 0
This gives x = 25, which means the length is also 25, so the area is maximized when it is a square
The maximum area is 25*25 = 625 in^2

Question 568749: Deon has 12 milliliters of a 5% solution. He also has a solution that has a concentration of 30%. How many milliliters of the 30% solution does Deon need to add to the 5% solution to obtain a 20% solution?
Found 2 solutions by mananth, stanbon:
Answer by mananth(10539)   (Show Source):
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------------------------ percent ---------------- quantity
Solution Type I 12 ---------------- 5 ml
solution type II 30 ---------------- x ml
Mixture 20 ---------------- 5 + x ml
The sum of individual contents of the two types of components =content in mixture
12*5+30x=20(5+x)
60+30x =100+20x
30x-20x=100-60
10x=40
/10
x=4 ml of solution type II

m.ananth@hotmail.ca

Answer by stanbon(48502)   (Show Source):
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Deon has 12 milliliters of a 5% solution. He also has a solution that has a concentration of 30%. How many milliliters of the 30% solution does Deon need to add to the 5% solution to obtain a 20% solution?
-----
Equation:
active + active = active
0.05*12 + 0.30x = 0.20(12+x)
----
Multiply thru by 100 to get:
5*12 + 30x = 20*12 + 20x
10x = 15*12
x = (3/2)12
x = 18 ml (amt of 30% solution needed)
===================
Cheers,
Stan H.
===================

Question 568617: Seven less than twice a number is greater than the number increased by 3.
Answer by nyc_function(2626)   (Show Source):
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2x - 7 = x + 3

2x - x = 7 + 3

x = 10

Question 568392: A says to B, If you give me $12, we will have and equal amount of money." Monte respons,"that may be true but if you give me $6, I will have twice as much as you.How much money does A and B each have?
Answer by htmentor(580)   (Show Source):
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A says to B, If you give me $12, we will have and equal amount of money." Monte respons,"that may be true but if you give me $6, I will have twice as much as you.How much money does A and B each have?
===================
Let A = the amount of money A has
Let B = the amount of money B has
If B gives A 12, then B now has B-12 dollars and A now has A+12, and these two amounts are equal:
A+12 = B-12
If A gives B 6, then B will have twice as much as A:
B+6 = 2(A-6)
So we have two equations and two unknowns. Solve using your favorite method.
Ans: A = 42, B = 66
Check: If B gives A 12, they will both have 54
If A gives B 6, then A will have 36 and B will have 72, twice as much

Question 568285: When Bert and Ernie merged their automobile dealerships, Bert had 10 more cars than Ernie. While 36% of Ernie's stock consisted of new cars, only 25% of Bert's stock consisted of new cars. If they had 33 new cars on the lot after the merger, then how many cars did each one have before the merger?
Answer by josmiceli(6769)   (Show Source):
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Let = number of cars Bert had
Let = number of cars Ernie had
given:
(1)
(2)
---------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
Bert had 60 cars
Ernie had 50 cars
check answer:
(2)
(2)
(2)
OK

Question 568206: A 1,500 kg car accelerates from 44 km/h to 80 km/h in 10 s. What was the net force exerted on the car?
I know that F=ma but I am confused about what to do because it asks for the net force do I add 44 and 88 or subtract the terms?
Answer by richard1234(4789)   (Show Source):
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First find the acceleration of the car. We have

(kilometers per hour, per second). However we want to convert kilometers per hour to meters per second. 1 kph is roughly .2778 m/s, and it turns out that 3.6 kph/s is exactly 1 m/s^2. So a = 1 m/s^2.

We use F = ma to obtain

Question 568113: How do you solve for t in this equation:
(t/E)+1=t/V
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
(t/E)+1=t/V
------------
t/V - t/E = 1
t*(1/V - 1/E) = 1
t = 1/(1/V - 1/E)
===========
You can:
t = 1/((E - V)/VE)
t = VE/(E - V)

Question 568100: How much 15% HCl must be mixed with 8% HCl to produce 60mL of 9% solution?
Answer by stanbon(48502)   (Show Source):
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How much 15% HCl must be mixed with 8% HCl to produce 60mL of 9% solution?
-----
HCL + HCL = HCL
----
0.15x + 0.08(60-x) = 0.9*60mL
----
Multiply thru by 100 to get:
15x + 8*60-8x = 9*60
---
7x = 60
x = 8.5714 mL (amt. of 15% solution needed)
====
Cheers,
Stan H.
=============

Question 568034: what is the integer x which is satisfies 10^x < (1/2)(3/4)(5/6)(7/8)....(99/100) < 10^(x+1)?
Answer by stanbon(48502)   (Show Source):
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what is the integer x which is satisfies 10^x < (1/2)(3/4)(5/6)(7/8)....(99/100) < 10^(x+1)?
----
That number in the middle is greater than zero and less than 1
x = -1
===============
Cheers,
Stan H.

Question 567917: A worker was paid $4.50 per hour for a 40-hour week. The worker was paid an additional $1.50 per hour for each hour over 40 hours per week.
How much did the worker earn in 3 weeks if he worked 43 hours the first week, 42 hours the second week, and 45 hours the third week?
Answer by josmiceli(6769)   (Show Source):
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The worker's overtime was hrs for 3 weeks
The worker's regular time was hrs

The worker earned $600 for 3 weeks

Question 567907: The gravitational attraction A between two masses varies inversely as the square of the distance between them. If the force of attraction is 2.25 lbs when the masses are 4 ft apart, what is the attraction when the masses are 6 ft apart?
My answer = 3 lbs.
Thank you.
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
The gravitational attraction A between two masses varies inversely as the square of the distance between them. If the force of attraction is 2.25 lbs when the masses are 4 ft apart, what is the attraction when the masses are 6 ft apart?
My answer = 3 lbs.
=================

F = 1 lb

Question 567908: It is necessary to have a 40% solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
My answer = 20 liters
Thanks!
Answer by nerdybill(5403)   (Show Source):
You can put this solution on YOUR website!
It is necessary to have a 40% solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
.
Let x = liters to be drained and replaced w/100% antifreeze
then
.20(50-x) + x = .40(50)
10-.20x + x = 20
10 + .80x = 20
.80x = 10
x = 10/.80
x = 12.5 liters

Question 567858: You are offered two different jobs selling dental supplies. One has an annual salary of $20,000 plus an end of year bonus of 1% of your total sales. The other has a salary of $15,000 and a year -end bonus of 2% of your sales. How much would you have to sell to have the jobs pay the exact same amount?
Equations: x represents:
y represents:
pay job 1 y =
pay job 2 y =
Solve the system:
Solution: If you would sell $_______________________ of equipment, both jobs would pay you $_____________________.
Analysis: If you were to sell $300,000 worth of equipment, which job would pay better? _______________. If you were to sell $700,000 worth of equipment, which job would pay better?___________________. If you sell $__________________ or more Job 2 would pay better.

Answer by mananth(10539)   (Show Source):
You can put this solution on YOUR website!
Let the sales be $x
Pay job 1 --20000 +0.01x
Pay job 2-- 15000+0.02x
earnings to be equal
20000+0.01x=15000+0.02x
20000-15000=0.02x-0.01x
5000= 0.01x
/0.01
x=500,000
Sales should be $ 500,000 for eranings to be the same
20000+0.01x=15000+0.02x
plug 300000 for x
20000+300000*0.01 ---------15000+0.02*300000
23000-----------21000
Pay job I will earn more
You can work out for $700,000

Question 567707: A merchant mixed 10 lb of a cinnamon tea with 5 lb of spice tea. The 15-pound mixture cost $40. A second mixture included 12 lb of the cinnamon tea and 8 lb of spice tea. The 20 lb mixture cost $54. Find the cost per pound of the cinnamon tea and the spice tea.
Answer by lwsshak3(2907)   (Show Source):
You can put this solution on YOUR website!
A merchant mixed 10 lb of a cinnamon tea with 5 lb of spice tea. The 15-pound mixture cost $40. A second mixture included 12 lb of the cinnamon tea and 8 lb of spice tea. The 20 lb mixture cost $54. Find the cost per pound of the cinnamon tea and the spice tea.
**
let x=cost per pound of cinnamon
let y=cost per pound of spice tea
..
10x+5y=40
12x+8y=54
..
80x+40y=320 (mult. by 8)
60x+40y=270 (mult. by 5)
subtract
20x=50
x=50/20=2.5
..
5y=40-10x=40-25=15
y=3
ans:
cost per pound of cinnamon=$2.50
cost per pound of spice tea=$3.00

Question 567732: I don't know what I did wrong. Hope you can help.
In 2005, the number of federal hazardous waste sites in Cali was 3 less than twice the number of sites in Washington. How many hazardous waste sites were there in Washington if there were 21 such sites in Calif?
In Washington, there were ____ federal hazardous waste sites.
I said 39. A friend of mine also said 39. The correct answer was 12.
21 * 2= 42
42 - 3 = 39
I am not sure what I am doing wrong.

Answer by stanbon(48502)   (Show Source):
You can put this solution on YOUR website!
In 2005, the number of federal hazardous waste sites in Cali was 3 less than twice the number of sites in Washington. How many hazardous waste sites were there in Washington if there were 21 such sites in Calif?
Equation:
c = 2w-3
21 = 2w-3
2w = 24
w = 12 (12 sites in Washington)
=====================
Cheers,
Stan H.
------------------
In Washington, there were ____ federal hazardous waste sites.

Question 567530: In the lab, Jim has two solutions that contain alcohol and is mixing them with each other. He uses milliliters less of Solution A than Solution B. Solution A is alcohol and Solution B is alcohol. How many milliliters of Solution B does he use, if the resulting mixture has milliliters of pure alcohol?
Answer by gumbug(1)   (Show Source):
You can put this solution on YOUR website!
a 75 0/0

Question 567475: Going into the final exams, which will count as two-thirds of the final grade, Mike has test scores of 86,80,84, and 90. What score does Mike need on the final in order to earn a B, whuch requires an average score of 80? What does he need to earn an A, which requires an average of 90?
Answer by lwsshak3(2907)   (Show Source):
You can put this solution on YOUR website!
Going into the final exams, which will count as two-thirds of the final grade, Mike has test scores of 86,80,84, and 90. What score does Mike need on the final in order to earn a B, which requires an average score of 80? What does he need to earn an A, which requires an average of 90?
**
Given:
final exam counts as 2/3 of the final score
previous test scores count as 1/3 of the final score
let x=score needed on final to get a B or A grade
..
(86+80+84+90)/4=85 (average of previous test scores)
To get a B grade:
85/3+2x/3=80
85+2x=240
2x=240-85=155
x=155/2=77.5
..
To get an A grade:
85/3+2x/3=90
85+2x=270
2x=270-85=185
x=185/2=92.5
..
ans:
Final score needed to earn an A: 92.5
Final score needed to earn a B: 77.5

Question 567233: train A travels 20mph slowr than Train B. It takes Train A 30min. longer than train B to travel 200 miles.
how long does it take train A to make the 200mile trip? how long does it take train B to travel 535 miles??
Found 2 solutions by lwsshak3, mananth:
Answer by lwsshak3(2907)   (Show Source):
You can put this solution on YOUR website!
train A travels 20mph slowr than Train B. It takes Train A 30min. longer than train B to travel 200 miles.
how long does it take train A to make the 200mile trip? how long does it take train B to travel 535 miles??
**
let x=speed(mph) of train B
x-20=speed(mph) of train A
travel time = distance/speed
..
200/(x-20)-200/x=30min=1/2 hr
LCD:2x(x-20)
2x(200)-200*2(x-20)=x(x-20)
400x-400x+8000=x^2-20x
x^2-20x-8000=0
(x-100)(x+80)=0
x+80=0
x=-80(reject, x>0)
or
x-100=0
x=100 mph (speed of train B)
x-20=80 mph (speed of train A)
..
travel time of train A=200/80=2.5 hrs
travel time of train B=535/100=5.35 hrs
.
ans:
time it takes train A to make the 200mile trip=2.5 hrs
time it take train B to travel 535 miles=5.35 hrs

Answer by mananth(10539)   (Show Source):
You can put this solution on YOUR website!
Train B speed = xmph
Train A speed = x-20 mph
Time taken by B = Time taken by A -1/2
t=d/r
200/x = 200/(x-20)-1/2
200/x -200/(x-20)=-1/2
LCD = x(x-20)
multiply equation by the LCD
200(x-20)-200*x=- 1/2 * x(x-20)
200x-4000-200x=-1/2*( x^2-20x)
multiply by -2
-400x+8000 +400x=x^2-20x
x^2-20x-8000=0
x^2-100x+80x-8000=0
x(x-100)+80(x-100)=0
(x-100)(x+80)=0
x=100 OR -80
Ignore negative since speed cannot be negative
spped of B is 100 mph
Time taken by B to travel 535 miles= 535/100
= 5.35 hours

Question 566955: Explain how you know a triangle can have side lengths measuring 11,
15 and 21.
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
Three positive numbers will uniquely determine a triangle (provided that they satisfy the triangle inequality, which they do in this case).

Question 567191: Things did not go quite as planned. You invested $10,250.00, part of it in stock that paid 12.5% annual interest. However, the rest of the money suffered a 6.7% loss. If the total annual income from both investments was $346.00, how much was invested at each rate?
Answer by stanbon(48502)   (Show Source):
You can put this solution on YOUR website!
You invested $10,250.00, part of it in stock that paid 12.5% annual interest. However, the rest of the money suffered a 6.7% loss. If the total annual income from both investments was $346.00, how much was invested at each rate?
----
Quantity Eq::: x + y = 10,250
Interest Eq::0.125x - 0.067y = 346
-----------------------------------
Multiply thru the Interest equation by 1000
Multiply thru the Quantity Eq. by 125
--------------------------
125x + 125y = 125*10,250
125x - 67y = 346000
---------------------------------------
Subtract and solve for "y":
192y = $935,250
y = $4871.09 (amt. invested at 6.7%
Solve for "x":
x + y = 10,250
x + 4671.09 = 10,250
x = $5378.91 (amt. invested at 12.5%
=========================================
Cheers,
Stan H.
==============

Question 566914: John, Paul, George, and Stuart were four school friends. After one particularly hard day's night, they went to see a movie together. After the first time, they began going regularly but on different schedules. (They even went on weekends.) John went every fourth day, Paul went every fifth day, George went every seventh day, and Stuart went every ninth day. How many days was it before all four went to the movies together again?
Thanks
Answer by ankor@dixie-net.com(12681)   (Show Source):
You can put this solution on YOUR website!
John went every fourth day,
Paul went every fifth day,
George went every seventh day, and
Stuart went every ninth day.
How many days was it before all four went to the movies together again?
:
What we want here is the Least common multile of 4, 5, 7, 9
The numbers do not have any common prime factors, therefore
4*5*7*9 = 1260 days before they all went to the movies together again

Question 566995: John, Paul, George, and Stuart were four school friends. After one particularly hard day's night, they went to see a movie together. After the first time, they began going regularly but on different schedules. (They even went on weekends.) John went every fourth day, Paul went every fifth day, George went every seventh day, and Stuart went every ninth day. How many days was it before all four went to the movies together again?
Answer by stanbon(48502)   (Show Source):
You can put this solution on YOUR website!
John, Paul, George, and Stuart were four school friends. After one particularly hard day's night, they went to see a movie together. After the first time, they began going regularly but on different schedules. (They even went on weekends.)
--------------------------------------------
John went every fourth day, Paul went every fifth day, George went every seventh day, and Stuart went every ninth day. How many days was it before all four went to the movies together again?
--------------------
Least common multiple: 4*5*7*9 = 1260 days
========================================
Cheers,
Stan H.
=============

Question 566889: Hello, I need help with this question. It says: "After Valerie is seated in a restaurant, she realizes that she only has $20. If she must pay 7% sales tax and wishes to leave a 15% tip on the total bill (meal plus tax) what is the maximum price of lunch she can order?" I've tried several ways to solve this, but never get the right answer. I've tried to add .15 to .07 and equal it to 20 for example
Answer by 505Zephyr(1)   (Show Source):
You can put this solution on YOUR website!
20*.07= 1.4
so 20+1.4= $21.40
20*.15= 3
so20+3= $23+1.40= $24.40