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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629, >>NextUnit_Conversion_Word_Problems/582944: You are trying to decide which of 2 cars to buy. An American made costs $14,500 and has a consumption of 28 miles/gallon. The other is Japanese, costs $21,700 and with a consumption of 19km/litre.
If the cost of petrol is $2.50 per gallon, estimate the number of miles you will need to drive the second car to compensate for the higher cost of the car.
1 solutions
Answer 372407 by ankor@dixie-net.com(15628)   on 2012-03-06 19:57:46 (Show Source):
You can put this solution on YOUR website!You are trying to decide which of 2 cars to buy.
An American made costs $14,500 and has a consumption of 28 miles/gallon.
The other is Japanese, costs $21,700 and with a consumption of 19km/litre.
If the cost of petrol is $2.50 per gallon, estimate the number of miles you will need to drive the second car to compensate for the higher cost of the car.
:
Change 19 km to mile
.6214(19) = 11.8066 mi/liter
Change to mi/gal
11.8066 * 3.785 = 44.688 = 44.7 mi/gal
:
Let m = no. of miles for the total cost of be the same
:
2.50*  + 14500 = 2.50*  + 21700
.0893m + 14500 = .0559m + 21700
.0893m - .0559m = 21700 - 14500
.0334m = 7200
m = 7200/.0334
m = 215,569 mi for the total cost of each to be about the same
:
:
See if that works out
Acost = 2.50*  + 14500
cost = $33,747
:
Jcost = 2.50*  + 21700
cost = $33.756
:
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Rational-functions/583032: a welder requires 25 hours to do a job. after the welder and an apprentice work on a job for 10 hours the wilder quits, the apprentice finishes the job in 17 hours. How long would it take the apprentice, working alone, to do the job
1 solutions
Answer 372363 by ankor@dixie-net.com(15628) on 2012-03-06 16:36:37 (Show Source):
You can put this solution on YOUR website!a welder requires 25 hours to do a job.
after the welder and an apprentice work on a job for 10 hours the wilder quits, the apprentice finishes the job in 17 hours.
How long would it take the apprentice, working alone, to do the job
:
Let a = time required by the apprentice to do the job
Let the completed job = 1
:
From the information given, we see the apprentice worked a total of 27 hrs
:
 +  = 1
multiply by 25a, results
10a + 25(27) = 25a
10a + 675 = 25a
675 = 25a - 10a
675 = 15a
a = 
a = 45 hrs, the apprentice working alone
|
Numbers_Word_Problems/582889: The sum of the 3 digits of an even number is 9. What is the number if its ten digits its 1 more than its ones digit?
1 solutions
Answer 372360 by ankor@dixie-net.com(15628) on 2012-03-06 16:21:02 (Show Source):
You can put this solution on YOUR website!The sum of the 3 digits of an even number is 9.
What is the number if its ten digits its 1 more than its ones digit?
:
Three digits, a, b, c
:
a + b + c = 9
:
b = c + 1
:
a + (c+1) + c = 9
a + 2c = 9 - 1
a + 2c = 8
a = -2c + 8
:
3 solutions
621
432; the only even number
243
|
Age_Word_Problems/582942: Tom is 3 times as old as his cousin Sam and 14 years older than his parrot Polly. In 4 years, Lucy will be half as old as Polly. How old is Tom ??
1 solutions
Answer 372316 by ankor@dixie-net.com(15628) on 2012-03-06 13:28:51 (Show Source):
You can put this solution on YOUR website!Tom is 3 times as old as his cousin Sam and 14 years older than his parrot Polly.
In 4 years, Lucy will be half as old as Polly. How old is Tom ??
:
Let t = Tom's age
Let s = Sam's age
Let p = parrot's age
Let L = Lucy's age
;
Write an equation for each statement:;
:
"Tom is 3 times as old as his cousin Sam"
t = 3s
;
" and 14 years older than his parrot Polly."
t = p + 14
:
"In 4 years, Lucy will be half as old as Polly."
L + 4 = .5(p+4)
L + 4 = .5p + 2
L = .5p + 2 - 4
L = .5p - 2
:
How old is Tom ??
:
A lot of unrelated facts here, all we know for sure is Tom is at least 15 years old and his age is multiple of 3, the parrot is an even number of years old in order for Lucy to be half it's age
:
Let's say Tom is 24, then Sam is 8, parrot is 10,
Find Lucy's age
L + 4 = .5(10+4)
L + 4 = 7
L = 7 - 4
Lucy is 3
;
Tom is 24 is one answer
|
Linear_Equations_And_Systems_Word_Problems/582880: need to come up with two equations, with x and y
A bricklayer lays an average of 150 bricks per hour. During a job, he is called away and replaced by a less experienced man, who averages 120 bricks per hour. The two men laid 930 bricks in 7 hours. How long did each work?
1 solutions
Answer 372270 by ankor@dixie-net.com(15628) on 2012-03-06 08:31:32 (Show Source):
You can put this solution on YOUR website!A bricklayer lays an average of 150 bricks per hour.
During a job, he is called away and replaced by a less experienced man, who averages 120 bricks per hour.
The two men laid 930 bricks in 7 hours. How long did each work?
:
Let x = time worked by the experienced bricklayer
Let y = time worked by apprentice
:
Time equation
x + y = 7
y = (7-x); use this form for substitution
:
Production equation
150x + 120y = 930
replace y with (7-x), find x
150x + 120(7-x) = 930
150x + 840 - 120x = 930
150x - 120x = 930 - 840
30x = 90
x = 90/30
x = 3 hrs worked the exp guy
:
You can find the hrs worked by the other guy. check solutions in the production equation
|
Miscellaneous_Word_Problems/582407: The cabels of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at the height of 10 feet ,idway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge?
1 solutions
Answer 372240 by ankor@dixie-net.com(15628) on 2012-03-05 21:55:25 (Show Source):
You can put this solution on YOUR website!The cables of a suspension bridge are in the shape of a parabola.
The towers supporting the cable are 400 feet apart and 100 feet high.
If the cables are at the height of 10 feet midway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge?
:
Use the given information to create a quadratic equation to represent this bridge
Using the form: ax^2 + bx + c = y
left side
x=0, y=100, therefore c=100
:
Midway
x=200, y=10
200^2a + 200b + 100 = 10
40000a + 200b = 10 - 100
40000a + 200b = -90
:
right end
x=400, y=100
400^2a + 400b + 100 = 100
160000a + 400b = 0
:
Multiply the midway equation by 2, subtract from the above
160000a + 400b = 0
80000a + 400b = -180
-----------------------subtraction eliminates b, find a
80000a = 180
a = 180/80000
a = .00225
find b
160000(.00225) + 400b = 0
360 + 400b = 0
400b = -360
b = -360/400
b = -.9
:
The equation: y = .00225x^2 - .9x + 100
looks like this
:
"what is the height of the cable at the point 50 feet from the center of the bridge?"
x = 200-50
x = 150
y = .00225(150^2) - .9(150) + 100
y = 15.625 ft above 0
:
x = 200 + 50
x = 250
do the same as we did above
|
Travel_Word_Problems/582554: It takes Sally three minutes to go one mile with the wind at her back. Then it takes her four minutes on the ride back with the wind against her. What is the rate of the speed of the wind? Please help me. I tried this and got the answer of one over twentyfour.
1 solutions
Answer 372230 by ankor@dixie-net.com(15628) on 2012-03-05 21:17:08 (Show Source):
You can put this solution on YOUR website!It takes Sally three minutes to go one mile with the wind at her back.
Then it takes her four minutes on the ride back with the wind against her.
What is the rate of the speed of the wind?
:
Assume they want the speeds in mph
:
Convert 1 mi in 3 min to mph
 = 20 mph effective speed with the wind
and
 = 15 mph effective speed against the wind
:
Let s = speed in still air
Let w = speed of the wind
:
s + w = 20
s - w = 15
-----------adding eliminates w, find s
2s = 35
s = 35/2
s = 17.5 mph in still air
:
Find the speed of the wind
17.5 + w = 20
w = 20 - 17.5
w = 2.5 mph is the rate of the wind
|
Expressions-with-variables/582398: please help me to grasp the concept of solving with elimination method.
-3x+4y=1
-6+6y=-3
4x-8y=48
11x+3y=105.5
8x+11y=-50
-32x-44y=-200
1 solutions
Answer 372204 by ankor@dixie-net.com(15628) on 2012-03-05 20:02:51 (Show Source):
You can put this solution on YOUR website!solving with elimination method.
-3x + 4y = 1
-6x + 6y =-3
the idea is to multiply one or both equations so that one variable has the same coefficient, ideally one is positive and the other negative
Multiply the 1st equation by -2, add to the 2nd equation
+6x - 8y = -2
-6x + 6y = -3
----------------Adding eliminates x, find y
0 + -2y = -5
y = 
y = +2.5
;
find x using the 1st equation
-3x + 4(2.5) = 1
-3x + 10 = 1
-3x = 1 - 10
-3x = -9
divide both sides by -3
x = 3
:
Check our solution in the 2nd equation
-6x + 6y = -3
-6(3) + 6(2.5) = -3
-18 + 15 = -3
:
:
4x - 8y = 48
11x + 3y = 105.5
multiply the 1st equation by 3, the 2nd equation by 8
12x - 24y = 144
88x + 24y = 844
-----------------adding eliminates y, find x
100x + 0 = 988
x = 988/100
x = 9.88
:
Find y using the 1st equation
4(9.88) - 8y = 48
39.52 - 8y = 48
-8y = 48 - 39.52
-8y = 8.48
y = 
y = -1.06
:
Check solution in the 2nd equation
11x + 3y = 105.5
11(9.88) + 3(-1.06) = 105.5
108.68 - 3.18 = 105.5
:
:
8x + 11y = -50
-32x -44y =-200
multiply the 1st equation by 4, add to the 2nd equation
+32x + 44y = -200
-32x -44y = -200
--------------
note that every term cancels, the two equations are equivalent, dependent
|
Geometry_Word_Problems/582370: I have bee trying to figure this problem out for hours. Please help.
From 2005 to 2007, enrollment at a university decreased by 2%. If enrollment in 2007 was 8771 students, what was the enrollment in 2005?
1 solutions
Answer 372127 by ankor@dixie-net.com(15628) on 2012-03-05 18:16:44 (Show Source):
You can put this solution on YOUR website!From 2005 to 2007, enrollment at a university decreased by 2%.
If enrollment in 2007 was 8771 students, what was the enrollment in 2005?
:
Let x = enrollment in 2005
the multiplier for 2% drop is .98
:
This occurred for 2 yrs so we have:
:
x*.98^2 = 8771
x * .9604
x = 
x = 9,133 students in 2005
|
Trigonometry-basics/582488: Can you please exlpain step by step how to solve 2/x-3 - 4/x+3 = 8/x^2-9
1 solutions
Answer 372102 by ankor@dixie-net.com(15628) on 2012-03-05 17:25:57 (Show Source):
You can put this solution on YOUR website! = 
The third denominator is the difference of squares and can be factored to;
= 
Multiply each term by (x-3)(x+3)
(x-3)(x+3)*  - (x-3)(x+3)*  = (x-3)(x+3)*
Cancel the denominators and you have:
2(x+3) - 4(x-3) = 8
2x + 6 - 4x + 12 = 8
2x - 4x + 18 = 8
-2x = 8 - 18
-2x = -10
x = +5
:
:
Check this in the original problem for x = 5
 = 
|
Travel_Word_Problems/582282: You drive to your Nana’s at a speed of 20 km/h and then come home at a speed to 30 km/h. What is the average speed for the whole trip?
1 solutions
Answer 372076 by ankor@dixie-net.com(15628) on 2012-03-05 16:06:12 (Show Source):
You can put this solution on YOUR website!You drive to your Nana’s at a speed of 20 km/h and then come home at a speed to 30 km/h.
What is the average speed for the whole trip?
:
Let a = average speed for the whole trip
:
let d = distance one way
then
2d = distance for the whole trip
:
write a time equation; time = dist/speed
:
there time + return time = total time
 +  = 
multiply by 60a
60a* + 60a* = 60a
cancel the denominator, results:
3ad + 2ad = 60(2d)
5ad = 120d
Divide both side by d
5a = 120
a = 120/5
a = 24 mph average speed for the whole trip
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Rate-of-work-word-problems/582315: if 3 men can repair the house in 20 days,how many days can 5 men do the same job?
1 solutions
Answer 372068 by ankor@dixie-net.com(15628) on 2012-03-05 14:27:49 (Show Source):
You can put this solution on YOUR website!if 3 men can repair the house in 20 days, how many days can 5 men do the same job?
:
Find how many man-days to complete the job.
3*20 = 60 man-days
:
" how many days can 5 men do the same job?"
let d = no. of days required by 5 men to do it
5d = 60
d = 60/5
d = 12 days
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Linear-equations/582345: Find the equation of the line that contains the point (4,-2). and has slope 3/4. I started with using the formula y=mx+b. I set it up as -2=3/4 (4)+b but I can't finish it from here.
1 solutions
Answer 372066 by ankor@dixie-net.com(15628) on 2012-03-05 14:19:21 (Show Source):
You can put this solution on YOUR website!Find the equation of the line that contains the point (4,-2). and has slope 3/4.
:
mx + b = y
Replace m, x, y
 (4) + b = -2
3 + b = - 2
b = - 2 - 3
b = -5
:
y = x - 5 is the equation
:
You can check this, replace x with 4, in the equation and see if y = -2
|
Travel_Word_Problems/582213: After about 8 hours of a steady wind, the height (y) of waves in the ocean is linearly related to the duration of time (x) the wind has been blowing. During a storm with 40-knot winds, the wave height after 8 hours was found to be 22 feet, and after 23 hours it was 41 feet.
(a) Write a linear equation that relates the height to time.
(b) How long will the wind have been blowing for the waves to be 60 feet heigh?
1 solutions
Answer 372058 by ankor@dixie-net.com(15628) on 2012-03-05 13:30:15 (Show Source):
You can put this solution on YOUR website!After about 8 hours of a steady wind, the height (y) of waves in the ocean is linearly related to the duration of time (x) the wind has been blowing.
During a storm with 40-knot winds, the wave height after 8 hours was found to be 22 feet, and after 23 hours it was 41 feet.
:
(a) Write a linear equation that relates the height to time.
find the slope: m = 
assign the values as follow
x1=8, y1=22
x2=23, y2=41
:
Find the slope (m)
m = =  =  is the slope
:
Use the point/slope form to create an equation: y - y1 = m(x - x1)
y - 22 = (x - 8)
y - 22 = x - 
y = x - + 22
y = x - + 
y = x +  ; is the equation
:
(b) How long will the wind have been blowing for the waves to be 60 feet height?
x + = 60
multiply by 15 to get rid of the denominators
19x + 178 = 15(60)
19x = 900 - 178
19x = 722
x = 
x = 38 hrs to reach 60 ft waves
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Percentage-and-ratio-word-problems/582334: A motorcycle breaks down and the rider must walk the rest of the way to work. The motorcycle was being driven at 45mph, and the rider walks at a speed of 6mph. The distance from home to work is 25miles, and the time for the trip was 2hr. How far did the motorcyle go before it broke down?
1 solutions
Answer 372032 by ankor@dixie-net.com(15628) on 2012-03-05 08:29:36 (Show Source):
You can put this solution on YOUR website!A motorcycle breaks down and the rider must walk the rest of the way to work.
The motorcycle was being driven at 45mph, and the rider walks at a speed of 6mph.
The distance from home to work is 25miles, and the time for the trip was 2hr.
How far did the motorcycle go before it broke down?
:
Let m = distance rode on the motorcycle
then
(25-m) = distance he walked
:
Write a time equation: time = dist/speed
:
ride time + walk time = 2 hrs
 +  = 2
multiply by LCM of the denominators, 90 will do it, results:
2m + 15(25-m) = 90(2)
:
2m + 375 - 15m = 180
2m - 15 m = 180 - 375
-13m = -195
13m = 195
m = 195/13
m = 15 mi on the motorcycle
:
:
Check this by finding the actual times
15/45 = .33
10/6 = 1.67
------------
tot time: 2 hrs
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Polynomials-and-rational-expressions/582207: Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 7x3 + 6x2 – 6x – 3. The shop estimates their costs for that quarter to be given by 6x2 – 9x + 9. For the second quarter, find and simplify a polynomial that will represent their profit.
1 solutions
Answer 372031 by ankor@dixie-net.com(15628) on 2012-03-05 08:16:09 (Show Source):
You can put this solution on YOUR website!Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 7x3 + 6x2 – 6x – 3.
The shop estimates their costs for that quarter to be given by 6x2 – 9x + 9.
For the second quarter, find and simplify a polynomial that will represent their profit.
:
Revenue: r(x) = 7x^3 + 6x^2 - 6x - 3
Costs: c(x) = 6x^2 - 9x + 9
:
Profit (p) = Revenue - cost, therefore:
p(x) = (7x^3 + 6x^2 - 6x - 3) - (6x^2 - 9x + 9)
removing the brackets
p(x) = 7x^3 + 6x^2 - 6x - 3 - 6x^2 + 9x - 9
combine like terms
p(x) = 7x^3 + 6x^2 - 6x^2 - 6x + 9x - 3 - 9
:
p(x) = 7x^3 + 3x - 12; is the profit
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Exponents/582199: im so confused!! im in grade 10 foundations math and were working on rational exponents. is the question is to evaluate 16 & 3/4 i change it too the square root of 16 to the power of 3 and then the four goes on the left hand side outside of the square root symbol. i get 64 but then i dont know what to do with the four. do i divide 64 by four? it wasnt expained...
1 solutions
Answer 371996 by ankor@dixie-net.com(15628) on 2012-03-04 21:52:20 (Show Source):
You can put this solution on YOUR website!16^(3/4)
find the 4th root of 16, that is 2, right
then
2^3 which is 8
:
You can do it the other way too, but will need a calc
find 16^3 = 4096
then
find the 4th root of 4096,  on a calc = 8 also
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Age_Word_Problems/581574: The sum of the ages of Mr. Smith, Ms. Smith and their son, Tommy Smith, is 74. Ten years ago, this sum was 47. How old is Ms. Smith now if Mr. Smith is 28 years older than Tommy?
can you explain and show how you did the problem?
thanks
1 solutions
Answer 371993 by ankor@dixie-net.com(15628) on 2012-03-04 21:43:28 (Show Source):
You can put this solution on YOUR website!Write an equation for each statement:
:
The sum of the ages of Mr. Smith, Ms. Smith and their son, Tommy Smith, is 74.
a + b + c = 74
:
Ten years ago, this sum was 47.
(a-10) + (b-10) + (c-10) = 47
a + b + c - 30 = 47
a + b + c = 47 + 30
a + b + c = 77, but how could this be when above the sum is 74
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Exponents/581597: Using the exponential correlation, how do I solve for x. Round to three decimal places.
1)log(4x+10)=3
2)1/2 log6 16x +5=8
3)In(x+4)=-2
1 solutions
Answer 371991 by ankor@dixie-net.com(15628) on 2012-03-04 21:29:04 (Show Source):
You can put this solution on YOUR website!1)log(4x+10)=3
the exponent equiv of logs
4x + 10 = 10^3
4x + 10 = 1000
4x = 1000 - 10
4x = 990
x = 990/4
x = 247.5
:
2)1/2 log6 16x +5 = 8
not sure what you mean here, but will assume this
 log6(16x) = 8 - 5
log6(16x) = 3
multiply both sides by 2
log6(16x) = 6
16x = 
16x = 46656
x = 46656/16
x = 2916
:
3)In(x+4) = -2
x + 4 = e^-2
x + 4 = .1353
x = .1353 - 4
x = -3.864
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Rectangles/581883: The problem is, "The length of a rectangle exceeds it's width by 3 meters. The perimeter is 58 meters. Find the dimensions." I tried using subsitutions, but I got stuck and didn't get an answer. What do I do?
1 solutions
Answer 371990 by ankor@dixie-net.com(15628) on 2012-03-04 21:11:48 (Show Source):
You can put this solution on YOUR website!"The length of a rectangle exceeds it's width by 3 meters.
The perimeter is 58 meters. Find the dimensions."
:
The perimeter: 2L + 2W = 58
We can simplify this, divide by 2, and you have
L + W = 29
:
We know: L = (W+3)
:
(W+3) + W = 29
2W = 29 - 3
2W = 26
W = 13 is the width
then
13 + 3 = 16 is the Length
;
Now you check this in the perimeter equation
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Numbers_Word_Problems/582054: Batman, Robin, Superman, and the Joker shared $60. Batman received ½ of the total amount of money Robin, Superman, and the Joker received. Robin received 2/3 of the total amount of money Superman and the Joker received. Superman received 3 times as much as the Joker. A) How much money did Batman receive? B) How much more money did Robin receive than the Joker?
1 solutions
Answer 371986 by ankor@dixie-net.com(15628) on 2012-03-04 21:06:29 (Show Source):
You can put this solution on YOUR website!Write an equation for each statement, and see what we have here:
Batman, Robin, Superman, and the Joker shared $60.
b + r + s + j = 60
:
Batman received ½ of the total amount of money Robin, Superman, and the Joker received.
b = .5(r+s+j)
multiply by 2
2b = (r+s+j)
:
Robin received 2/3 of the total amount of money Superman and the Joker received.
r =  (s+j)
:
Superman received 3 times as much as the Joker.
s = 3j
:
A) How much money did Batman receive?
We can replace r+s+j with 2b in the 1st equation
b + 2b = 60
3b = 60
b = $20 for Batman
:
Now we know: r + s + j = 40
replace s with 3j
r + 3j + j = 40
r + 4j = 40
r = (40-4j)
:
Take the equation r = (s+j)
replace r with (40-4j), replace s with 3j
40-4j = (3j + j)
3(40-4j) = 2(4j); multiplied both sides by 3
120 - 12j = 8j
120 = 8j + 12j
120 = 20j
j = $6 for the poor Joker
:
r = 40 - 4(6)
r = $16 for Robin
:
B) How much more money did Robin receive than the Joker?
$10
;
:
Find s so we can check this out
s = 3(6)
s = $18 for Superman
:
20 + 16 + 18 + 6 = $60
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Rational-functions/582046: I am so lost, i could really use some major help!!
I know i have to factor... (x ) (x ) = 0
Can you please show & explain how to do them..
i know its kind of alot but i have a test tomorrow :/
But i have no clue how to even set problems like these up..
1. x+2/x = 2x+4/3
2. 4/x+1 = x-1/x+5
3. x/2x+1 = 2x/x+2
4. x/5 = -4/x-9
5. x^2 + 3/7x = x+1/6
Thankkk you sooo muchhh!!!!
1 solutions
Answer 371975 by ankor@dixie-net.com(15628) on 2012-03-04 20:26:20 (Show Source):
You can put this solution on YOUR website!1.  = 
Since you have single fractions on each side of the =, you can cross multiply
3(x+2) = x(2x+4)
3x + 6 = 2x^2 + 4x
arrange as a quadratic equation on the right
0 = 2x^2 + 4x - 3x - 6
0 = 2x^2 + x - 6
the will factor to
(2x-3)(x+2) = 0
two solutions
2x = 3
x = 1.5
and
x = -2
You should check all our solutions in original problems
:
2.  = 
Cross multiply
4(x+5) = (x+1)(x-1)
4x + 20 = x^2 + x - x - 1
0 = x^2 - 4x - 1 - 20
0 = x^2 - 4x - 21
Factors to
(x-7)(x+3) = 0
x = +7
x = -3
:
Do 3 and 4 the same way
3. x/2x+1 = 2x/x+2
4. x/5 = -4/x-9
:
I am not sure what you mean in this one, use brackets to clarify things here
5. x^2 + 3/7x = x+1/6
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Linear-equations/582012: My assignment was to collect data on 1 cup of broccoli and 1 cup of corn. The amount of calcium in one serving of broccoli is 62.4 mg and 1 mg of iron; in corn there is 5.4 mg of calcium and .6 mg of iron. The RDV for calcium a day is 1000 mg and for iron it is 18 mg. I need to construct and solve a linear system of two equations that would give me the amount of each food that would give me the full recommended values of calcium and iron. Here is the set up for calcium and I ended up with a negative amount:
x + y = 1000
62.4x + 5.4y = 1000
to solve for x x = -y + 1000
62.4(-y + 1000) + 5.4y = 1000
-62.4y + 62400 + 5.4y = 1000
- 62400 = -62400
-62.4y + 5.4y = 61400
-57y = - 61400
y = 1077
x + 1077 = 1000
- 1077 = -1077
x = -77
Can you tell me where I am going wrong?
1 solutions
Answer 371958 by ankor@dixie-net.com(15628) on 2012-03-04 19:24:33 (Show Source):
You can put this solution on YOUR website!My assignment was to collect data on 1 cup of broccoli and 1 cup of corn.
The amount of calcium in one serving of broccoli is 62.4 mg and 1 mg of iron; in corn there is 5.4 mg of calcium and .6 mg of iron.
The RDV for calcium a day is 1000 mg and for iron it is 18 mg.
I need to construct and solve a linear system of two equations that would give me the amount of each food that would give me the full recommended values of calcium and iron
:
x = servings of broc
y = servings of corn
:
Calcium: 62.4x + 5.4y = 1000
:
Iron: 1x + .6y = 18
this equation is easy to arrange for substitution
x = (18-.6y)
:
Replace x with (18-.6y) in the calcium equation
62.4(18-.6y) + 5.4y = 1000
1123.2 - 37.44y + 5.4y = 1000
-32.04y = 1000 - 1123.2
y = 
y = +3.845 ~ 4 servings of corn
:
Find x
x = 18 - .6(3.845)
x = 15.692 ~ 16 servings of broc (ugh!)
:
:
See if that checks out for calcium
62.4(16) + 5.4(4) =
998 + 22 = 1020 mg, high because we rounded the servings up
:
You can check the iron requirement
16 + .6(4)
:
I think you went wrong because you did not write an equation for the iron requirement of 18 mg
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Miscellaneous_Word_Problems/582103: One solar heating panel can raise the temperature of a quantity of water 1 degree in 30 minutes. A second solar heating panel can raise the temperature of the same quantity of water 1 degree in 45 minutes. How long would it take to raise the temperature of that quantity of water 1 degree when both solar panels are operating?
1 solutions
Answer 371950 by ankor@dixie-net.com(15628) on 2012-03-04 18:56:02 (Show Source):
You can put this solution on YOUR website!One solar heating panel can raise the temperature of a quantity of water 1 degree in 30 minutes.
A second solar heating panel can raise the temperature of the same quantity of water 1 degree in 45 minutes.
How long would it take to raise the temperature of that quantity of water 1 degree with both solar panels
:
Treat this as a "shared work" equation
:
let t = time required when both panels are used
let the completed job = 1 (raising a qty of water 1 degree)
:
 +  = 1
multiply by 90, to clear the denominators, results
3t + 2t = 90
5t = 90
t = 90/5
t = 18 min working together
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Miscellaneous_Word_Problems/581974: The krane children were born two years apart when Michael, the youngest of the six krane chldren was 1 year old. The sum of the their ages of all the children was 1+3+5+7+9+11 or 36, a perfect square. how many years old was Michael the next time the sum of the children's ages was a perfect square?
1 solutions
Answer 371945 by ankor@dixie-net.com(15628) on 2012-03-04 18:46:59 (Show Source):
You can put this solution on YOUR website!The krane children were born two years apart when Michael, the youngest of the six krane chldren was 1 year old.
The sum of the their ages of all the children was 1+3+5+7+9+11 or 36, a perfect square.
how many years old was Michael the next time the sum of the children's ages was a perfect square?
:
Note that 36/3 = 12
1 + 11 = 12
3 + 9 = 12
5 + 7 = 12
:
Using that knowledge find the next square that is even, and can be evenly divided by 3
not 49
not 64
not 81
not 100
not 121
try 144
144/3 = 48
23 + 25 = 48
21 + 27 = 48
19 + 29 = 48
:
Micheal is 19
19 + 21 + 23 + 25 + 27 + 29 = 144 is the next perfect square
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Percentage-and-ratio-word-problems/582084: How would I set up this word problem?
"The sum of a number and its reciprocal is 29/10. Find the number."
The eguation that I have tried looks like this:
x + 1/x=29/10
By the way the 1/x, for example, represents 1 over x.
1 solutions
Answer 371934 by ankor@dixie-net.com(15628) on 2012-03-04 18:16:45 (Show Source):
You can put this solution on YOUR website!x +  =  , just like you have it
multiply thru by 10x, cancel the denominators and you have:
10x(x) + 10 = 29x
10x^2 - 29x + 10 = 0; a quadratic equation
Use the quadratic formula, but this will factor to
(5x - 2)(2x - 5) = 0
two solutions
5x = 2
x = 
and
2x = 5
x =  , note they are the reciprocal of each other
:
:
Check with x =
+ =
 +  =
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Mixture_Word_Problems/582000: Please help me solve the following,I am stumped. One canned juice drink is 25% orange juice, another is 10% orange juice. How many liters of each should be mixed together in order to get 15 liters that is 14% orange juice?
Thank you for your help
1 solutions
Answer 371920 by ankor@dixie-net.com(15628) on 2012-03-04 16:51:36 (Show Source):
You can put this solution on YOUR website!One canned juice drink is 25% orange juice, another is 10% orange juice.
How many liters of each should be mixed together in order to get 15 liters that is 14% orange juice?
:
Two equations:
:
Total amt of juice
a + b = 15
b = (15-a); use this form for substitution
:
Percent juice amt
.25a + .10b = .14(15)
replace b with (15-a)
.25a + .10(15-a) = 2.1
.25a + 1.5 - .10a = 2.1
.25a - .10a = 2.1 - 1.5
.15a = .6
a = .6/.15
a = 4 liter so 25% juice
:
you can find b, the amt of 10% juice
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