# Questions on Word Problems: Evaluation, Substitution answered by real tutors!

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 Word Problems: Evaluation, Substitution Solvers Lessons Answers archive Quiz In Depth

Question 751364: An amusement park charges one admission price for adults and another admission price for children under 12. The Smoke family has two adults and three children under 12. The cost for their admission to the amusement park is $80. The Chalmers family has three adults and one child under 12. Their total admission cost is$99. What is the admission price for an adult and the admission price for a child?
You can put this solution on YOUR website!
Child price, c.

The Smoke family
2a+3c=80
The Chalmers family
3a+1*c=99

System of Equations:

(2 3 80)
(3 1 99)

(2 3 80)
(9 3 297)

(9 3 297)
(2 3 80)
Subtract second line from the first line: (7 0 217) meaning 7a=217
.
You can either original equation to find c.

Question 750267: An ice cream container is cylindrical with diameter 30cm and height 50cm and is filled with ice
cream. The ice cream scoop makes ice cream scoops of diameter 6cm. How many one scoop
cones can be made from one cylinder of ice cream?

You can put this solution on YOUR website!
Your cylinder has a base radius of 15cm, πr^2 is the base area, or 225π cm^2.
Multiply by the height to get volume 225π * 50 = 11,250π cm^3.
A sphere has v=4/3πr^3 or 4/3∏(3)^3 = 36π cm^3
The π cancels, and we are left with 11,250/36 = 312.5 scoops.

Question 749223: Solution A is 12% acid and Solution B is 4% acid. If a technician wants to mi them to make 60 liters of Solution C which is 10% acid, how many liters of each should be mixed together?
You can put this solution on YOUR website!
{amount of acid from A plus amount of acid from B}/{volume of solution C} = {concentration of solution C}

H = 12%, for solution A
L = 4%, for solution B
T = 10 %, wanted as solution C
M = 60 liters solution C
u = volume to use solution A
v = volume to use solution B

Solve the system for u and v, and then substitute the known values to compute u and v.

Question 749229: Solution A is 12% acid and Solution B is 4% acid. If a technician wants to mix them to make 60 liters of Solution C which is 10% acid, how many liters of each should be mixed together? I REALLY need help!!! n
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Solution A is 12% acid and Solution B is 4% acid. If a technician wants to mix them to make 60 liters of Solution C which is 10% acid, how many liters of each should be mixed together?
-------------
12A + 4B = 60*10 total acid
A + B = 60 total solution

Question 749244: A chemical technician had Solution A which is 10% and SOlution B which is 6% acid. If the technician wants to mis both solutions to mkae 100 Liters of Solution C which is 7% acid, how many liters of each should be mixed together? Solve the system by using substitution. I REALLY need some help!!!
You can put this solution on YOUR website!

You need liters of A and liters of B.

And

But since , we know that , so

Solve for and then calculate

By the way, precisely how much more desperate for help are you if you write "REALLY" in all caps as opposed to just writing "really", or not using "really" at all?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 749228: Solution A is 12% acid and Solution B is 4% acid. If a technician wants to mix them to make 60 liters of Solution C which is 10% acid, how many liters of each should be mixed together? I REALLY need help!!!
You can put this solution on YOUR website!
Let = liters of solution A needed
Let = liters of solution B needed
= liters of acid in solution A
= liters of acid in solution B
---------------------------------
(1)
(2)
----------------------------
(2)
(2)
Multiply both sides of (1) by and
subtract (1) from (2)
-----------------
(2)
(1)

and, since
(1)
(1)
(1)
45 liters of solution A are needed
15 liters of solution B are needed
check:
(2)
(2)
(2)
(2)
(2)
OK

Question 749208: This is a word problem. Solution A is 8% and Solution B is 4%. If a technician wans to mix them to make 150 liters of Solution C which is 6% acid, how many liters of each should be mixed together! I REALLY need help!
You can put this solution on YOUR website!
This is a word problem. Solution A is 8% and Solution B is 4%. If a technician wans to mix them to make 150 liters of Solution C which is 6% acid, how many liters of each should be mixed together!
---------
Equation:
acid + acid = acid
0.08x + 0.04(150-x) = 0.06*150
------
8x + 4*150 - 4x = 6*150
----
4x = 2*150
x = 75 liters (amt. of 8% solution needed)
150-x = 75 liters (amt. of 4% solution needed)
====================
Cheers,
Stan H.
====================

Question 748230: Luke is riding his bicycle on a circular track. If he completes 10 revolutions in 5 minutes, what is his angular speed in radians per second?
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Luke is riding his bicycle on a circular track. If he completes 10 revolutions in 5 minutes, what is his angular speed in radians per second?
------------------
10 revs = 10*2pi = 20pi radians
5 mins = 300 seconds

Question 748001: What is the conclusion of the statement
If x^2 = 4, then x=-2 or x=2

You can put this solution on YOUR website!

In conditional statements, the part the is the , and the part is the .
If hypothesis is true, then so is the conclusion.
and
the is or

Question 747692: Michael sold a total of 320 tickets at a fair. The money recived was $1255. Each adult ticket was$5 and each child ticket was $2. How many adult tickets did he sell. Answer by Cromlix(337) (Show Source): You can put this solution on YOUR website! x + y = 320........(1) 5x + 2y = 1255.....(2) Multiply (1) by 2 2x + 2y = 640 5x + 2y = 1255 Subtract -3x = -615 x = 205 Substitute x =205 in (1) 205 + y = 320 y = 320 - 205 y = 115 So he sold 205 Adult tickets and 115 Children's tickets Question 746303: A bistro has decided to open an outdoor eating area along one wall of the building. The outdoor area will be rectangular. Assume the restaurant wants to maximize the outdoor area. A) Suppose there is 160 feet of fencing available for the three sides that require fencing. Write an equation to model this situation and explain your work B) How long will the longest side of the fence be? C) What is the maximum area? Answer by Cromlix(337) (Show Source): You can put this solution on YOUR website! using xm for the breadth of the bistro and l for the length. l = 160 - 2x for the perimeter. The area = l x b = l x b = (160 - 2x)x A(x) = 160x - 2x^2 A'(x) = 160 - 4x (Differentiated) A'(x) = 0 160 - 4x = 0 - 4x = -160 x = 4 Using nature table: - 4 + 160 -4x + 0 - therefore x = 4 is a maximum. Longest side will be 160 - 4x 160 - 16 = 144 feet Maximum area = 160x - 2x^2 160(4) - 2(4)^2 640 - 32 608 ft^2 Question 745957: Square or Cube? Find at least one positive integral solution to the equation: (integral means x and y must be integers) (-x)²y - y³ = 105. Please explain your response, because I don't have a clue. Thanks for your help! Answer by Edwin McCravy(8909) (Show Source): You can put this solution on YOUR website!  (-x)²y - y³ = 105 x²y - y³ = 105 y(x² - y²) = 105 y(x - y)(x + y) = 105 So we have three factors y, x-y, and x+y having product 105. Since 105 = 1·3·5·7 either one of those factors is 1 or none are. If none of the three are 1 then {y, x-y, x+y} = {3,5,7}. x+y must be the largest, 7 so {y, x-y} = {3,5}. The sum of the two elements of the left set must equal the sum of the two elements on the right set, so y + x-y = 3+5 x = 8 But that's impossible since the largest factor x+y is only 7 So one of those factors must be 1. Let's try y=1 y(x - y)(x + y) = 105 1(x - 1)(x + 1) = 105 x² - 1 = 105 x² = 106 x = √106 which is not an integer. So the first factor y cannot be 1. The largest factor x+y cannot be 1, so the second factor x-y must be 1, x-y = 1, so we have y = x-1, Substituting that: y(x - y)(x + y) = 105 (x - 1)(1)(x + x-1) = 105 (x - 1)(2x - 1) = 105 2x² - 3x + 1 = 105 2x² - 3x - 104 = 0 (x-8)(2x+13) = 0 So x - 8 = 0, 2x + 13 = 0 x = 8 2x = -13 x = (discard) So we have x = 8, and since y = x-1 = 8-1 = 7 So the only solution with positive integers is x = 8, y = 7. Checking: (-x)²y - y³ = 105 (-8)²7 - 7³ = 105 64·7 - 343 = 105 448 - 343 = 105 105 = 105 Edwin Question 743064: A family has two cars. The first car has a fuel efficiency of miles per gallon of gas and the second has a fuel efficiency of miles per gallon of gas. During one particular week, the two cars went a combined total of miles, for a total gas consumption of gallons. How many gallons were consumed by each of the two cars that week? Answer by ankor@dixie-net.com(15650) (Show Source): You can put this solution on YOUR website! You have to give us specific values for mpg, gallons, and distance driven Question 743170: 7,700.00 is 20% on what whole number? Answer by rfer(12657) (Show Source): You can put this solution on YOUR website! 7700/0.20=38,500 Question 742477: A candy company mixes 20% fat- content chocolate with a 15% fat- content chocolate to obtain 50 pounds of a 16% fat content chocolate. How many pounds of each type of chocolate should be used? (write 2 equations and solve this system of equations.) Answer by lwsshak3(6501) (Show Source): You can put this solution on YOUR website! A candy company mixes 20% fat- content chocolate with a 15% fat- content chocolate to obtain 50 pounds of a 16% fat content chocolate. How many pounds of each type of chocolate should be used? (write 2 equations and solve this system of equations.) *** let x=lbs of 20% fat chocolate to mix let y=lbs of 15% fat chocolate to mix .. 20%x+15%y=16%*50 x+y=50 y=50-x 20%x+15%(50-x)=16%*50 0.2x+7.5-0.15x=8 0.05x=0.5 x=10 y=50-x=40 lbs of 20% fat chocolate to mix=10 lbs of 15% fat chocolate to mix=40 Question 738795: On a rural highway a police officer sees a motorist run a red light at 50 mi/h and begins pursuit. At the instant the police officer passes through the intersection at 60 mi/h, the motorist is 0.2 mi down the road. When and where will the officer catch up to the motorist? Answer by fcabanski(874) (Show Source): You can put this solution on YOUR website! Distance = Rate x Time. The distance the officer has to make up is .2 miles. The speed at which the officer makes up the distance is the difference between the cars' speeds. That's 60 - 50 = 10 MPH. .2 = 10 * t .2/10 = t .02 hours = t = 1.2 minutes = 1 minute 12 seconds. Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.) Question 738793: Kerry asked a bank teller to cash a$390 check using $20 bills and$50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?
You can put this solution on YOUR website!
T are $20 bills. F are$50 bills

T + F = 15 Equation 1

20T + 50F = 390 Equation 2

Eq 1: T = 15-F (plug that into equation 2)

20(15-F) + 50F = 390

300 - 20F + 50F = 390

30F = 90

F = 3

T = 15-F = 15-3 = 12

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

Question 734765: Find three consecutive positive odd intergers such that the square of the smallest exceeds twice the largest by 7 | ONLY AN ALGEBRAIC SOLUTION WILL BE ACCEPTED?|
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Find three consecutive positive odd intergers such that the square of the smallest exceeds twice the largest by 7
------------------
1st: 2x-3
2nd: 2x-1
3rd: 2x+1
-------
Equation:
(2x-3)^2 = 2(2x+1)+7
------
4x^2 -12x + 9 = 4x+9
---
4x^2 -16x = 0
Factor:
4x(x-4) = 0
x = 0 or x = 4
----
If x = 0::
1st: -3
2nd: -1
3rd: 1
----
If x = 4
1st: 5
2nd: 7
3rd: 9
-----
Since you want positive odd only the x=4 set is acceptable.
=====================
Cheers,
Stan H.
=====================

Question 732504:

Carol took a math test and answered 16 of the 20 questions correctly. What was Carol’s percentage score on the test?

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16/20=.80=80% ans.

Question 730285: The population of a town increases according to the model: P(t)=2500e^(0.0293t), in which t is the time in years with t=0 corresponding to 1990. Use the model to estimate the population in
2025
(The 0.0293t is an entire exponent.)
An explanation would be really nice so that I can do future ones like this on my own.

Thanks!

Question 730003: The width of a rectangle is one third of the length. If the perimeter is 96 cm, find the width.

Question 729231: Working together, it takes two computers minutes to send out a company’s email. If it takes the slower computer minutes to do the job on its own, how long will it take the faster computer to do the job on its own?
You can put this solution on YOUR website!
Working together, it takes two computers minutes to send out a company’s email. If it takes the slower computer minutes to do the job on its own, how long will it take the faster computer to do the job on its own?
--------------
Since it's faster, it'll take fewer minutes.

Question 728450: Kerry asked the bank teller to cash a $390 check using$20 bills and $50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive? Answer by richwmiller(9135) (Show Source): You can put this solution on YOUR website! t+f=15, 20t+50f=390 trail and error method there have to be at least 2 20's and one 50 to make the 90 that's three bills we need 12 more we can't have just 2 fifty's so try 3 50's 3 50's would mean 12 20's 150 and 240 work Question 726847: five years ago i was 5 times older than my son, in 8 years time i will be 3 times older than my son. how old am i today? Answer by josmiceli(9676) (Show Source): You can put this solution on YOUR website! Let = my age today Let = my Son's age today given: (1) (2) ----------------------- (1) (1) and (2) (2) ------------------ Subtract (2) from (1) (1) (2) and (2) (2) (2) (2) The Father is 70 check: (1) (1) (1) (1) OK Question 726735: Twice my first number plus four times my second number is 100. what two numbers am i thinking of? Answer by checkley79(3050) (Show Source): You can put this solution on YOUR website! 2X+4Y=100 20&15 ARE ONE SET OF ANSWERS. 2*20+4*15=100 40+60=100 100=100 ################## 40&5 ARE ANOTHER SET OF ANSWERS. 2*40+4*5=100 80+20=100 100=100 Question 726665: 1.Traveling 900km by rail costs Rs 280, What would be the fare for a journey of 360km when a person travel by the same class. 2. 3/4 of the salary of per month is Rs 600. What is the salary per month? Answer by checkley79(3050) (Show Source): You can put this solution on YOUR website! 900/280=360/X CROSS MULTIPLY. 900X280*360 900X=100,800 X=100,800/900 X=112 rS. WOULD BE THE COST. ######################################## 3/4*X=600 3X/4=600 3X=4*600 3X=2,400 X=2,400/3 X=800 Rs. ANS. Question 726692: A 36 foot section of a log is cut into three pieces. The second piece is twice the length of the first and the third piece is equal to the length of the first two pieces. How long (in feet) is the longest section? Found 2 solutions by mbmodak, tanjo3: Answer by mbmodak(32) (Show Source): You can put this solution on YOUR website! Let first piece in length=x ft ---(1) second piece is twice the length of first piece second piece=2*x ft ---(2) third piece is equal to length of L(leng of 1st) + L(length of 2 nd) third piece=x+2x=3x ---(3) Total length of 3 pieces is 36 ft Adding(1)+(2)+(3) Total length=x+2x+3x x+2x+3x=36 6x=36 x=36/6=6 1st piece=6f 2nd piece=6*2=12 ft third piece=3*6=18 (total=6+12+18=36) Longest piece=18 Answer by tanjo3(25) (Show Source): You can put this solution on YOUR website! Let x be the length of the shortest log. Then 2x is the length of the second piece. Then (x+2x) is the length of the third and longest piece. Thus, the longest piece is (6+2(6)) = 18 ft. Question 726145: A catering company needs to provide 10 lbs of mixed nuts for a wedding reception. The couple has budgeted$42 for nuts. Peanuts cost $3.00/ lb and cashews cost$7.00/ lb. how many pounds each of peanuts and cashews should the catering company combine?
You can put this solution on YOUR website!
7x+3(10-x)=42
7x+30-3x=42
4x=42-30
4x=12
x=12/4
x=3 pounds of cashews are used.
10-3=7 pounds of peanut are used.
proof:
7*3+3*7=42
21+21=42
42=42

Question 725634: Is this easy to do????????????
You can put this solution on YOUR website!

Question 725106: Pls evaluate the following;
(-5)^0
I believe it is 1 but I am trying to remember the written formula.

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Just remember a simple rule:
"Any term, variable or number, with an exponent of 0 is = to 1

Question 724385: How do you solve..... I purchased 35 total pens. I purchased 4 times as many red ones than I did black ones. How do I write the equation that represents each color pen? r+b=35?
Found 2 solutions by josmiceli, Alan3354:
You can put this solution on YOUR website!
I think I know what they're after.
given:
(1)
(2)
--------------
Equation for red pens:
(1)
(2)

----------------
Equation for black pens
(1)
(2)

------------

You can put this solution on YOUR website!
How do you solve..... I purchased 35 total pens. I purchased 4 times as many red ones than I did black ones. How do I write the equation that represents each color pen? r+b=35?
=========================
r + b = 35
r = 4b
--------------------

Question 723804: the ratio of two numberds is 3:4. If the difference is 12 find its smaller number

You can put this solution on YOUR website!
Call the numbers x and y

x/y = 3/4 and y-x = 12 so y=x+12

Substitute that y value (x+12) into the proportion and then solve for x.

x/(x+12) = 3/4 ---> 4x = 3(x+12) = 3x + 36

x=36

y-36 = 12 ---> y = 48

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

Question 723755: You buy x keychains for $2 each and y snow globes for$3 each. You spend \$22 for 9 items. How many keychains do you buy?
You can put this solution on YOUR website!

Number of items
x+y=9
Value of items
2x+3y=22
solve them
you will get y=4 and x= 5

Question 723706: find all the roots and check answer. x 2nd + 5x-14=0
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x^2 + 5x-14=0
(x+7)(x-2)=0
x+7=0
x=-7 ans.
x-2=0
x=2 ans.
proofs:
-7^2+5(-7)-14=0
49-35=-14
-14=-14
2^2+5*2-14=0
4+10-14=0
14-14=0
0=0

Question 722637: (16x2 -56x+40)÷8 show by dividing

Question 720992: If a piece of wood is 5cm longer than a second piece and 3 divide by 4 of the second piece is equal to 3 divide 5 of the first.What is length of second piece
You can put this solution on YOUR website!
Always define a variable for the unknowns.
Let x = the length of the first piece of wood
Let y = the second piece of wood
Now you need TWO equations to find two unknowns.
The first part of the problem statement gives us
(1) x = y + 5.
The second part gives us
(2) (3/4)*y = (3/5)*x
Solve these two equations for (x,y). You can use any of the known methods, I'll use substitution for you.
Substitute the expression for x given by (1) into (2) and get
(3) (3/4)*y = (3/5)*(y + 5) or
(4) (3/4)*y = (3/5)*y + (3/5)*5 or
(5) [(3/4) - (3/5)]*y = 3 or
(6) [(15 - 12)/20]*y = 3 or
(7) (3/20)*y = 3 or
(8) y = 20
Now put y of (8) into (1) and get
(9) x = 20 + 5 or
(10) x = 25
Let's check these two values using (2).
Is ((3/4)*20 = (3/5)*25)?
Is (15 = 15)? Yes
Answer: The first piece of wood is 25cm and the second piece is 20cm.

Question 720361: the equation p=2t+2w gives the perimeter p of a rectangle with length l an width w.
You can put this solution on YOUR website!
the equation p=2t+2w gives the perimeter p of a rectangle with length l an width w.
------------------
That's possible.

Question 718743:
If 5 times the smaller of two numbers is subtracted from twice the larger, the result is 16. If the larger is increased by 3 times the smaller, the result is 63. Find the numbers.

You can put this solution on YOUR website!
LET X BE THE SMALLER & Y BE THE LARGER NUMBER.
2Y-5X=16
3X+Y=63 OR Y=63-3X
2(63-3X)-5X=16
126-6X-5X=16
-11X=16-126
-11X=-110
X=-110/-11
X=10 ANS. FOR THE SMALLER NUMBER.
Y=63-3*10
Y=63-30
Y=33 ANS. FOR THE LARGER NUMBER.
PROOF:
3*10+33=63
30+33=63
63=63

Question 717616: find the solution to each system by the substitution method. 3x-5y=7 x-4y= -7
You can put this solution on YOUR website!
x-4y=-7
x=4y-7
----------
3x-5y=7
3(4y-7)-5y=7
12y-21-5y=7
7y=28
y=28/7
y=4
-------------
3x-5(4)=7
3x-20=7
3x=27
x=27/3
x=9
(9,4)
----------------
x-4y=-7
9-16=-7
-7=-7

Question 717701: If possible, sole each sytem of equations. Use any method. If there is not a unique solution to a system, state a reason. 2x-8y=5 -6x+24y=15
Found 2 solutions by stanbon, josgarithmetic:
You can put this solution on YOUR website!
If possible, solve each sytem of equations. Use any method. If there is not a unique solution to a system, state a reason.
2x-8y=5
-6x+24y=15
-------
Multiply thru top equation by 3:
6x - 24y = 15
-6x+ 24y = 15
------
0 + 0 = 30
---
---
========================
Cheers,
Stan H.

You can put this solution on YOUR website!
The slopes are the same.

Second equation when divide by 3 is -2x+8y=5. Multiply this by -1 and it becomes 2x-8y=-5.

The lines are different, but parallel. No solution.

Question 717587: Parallel to x-y=4 and passing through (-3,2)
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given:
the line is parallel to or and passing through (,)
 Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (-3,2), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Combine like terms So the equation of the line that is parallel to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

Question 717593: When graphing y < -6, should the region below the line y = -6 be shaded or should the region above the line y= -6 be shaded?