SOLUTION: I need assistance with two separate word problems.
1) A car radiator contains 10 liters of a 30% solution. How many liters will have to be replaced with pure antifreeze if the r
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-> SOLUTION: I need assistance with two separate word problems.
1) A car radiator contains 10 liters of a 30% solution. How many liters will have to be replaced with pure antifreeze if the r
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Question 207220: I need assistance with two separate word problems.
1) A car radiator contains 10 liters of a 30% solution. How many liters will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze?
2) You are planning to start a business that will require an investment of $90,000. You have found some people who are willing to share equally in the venture. If you find three more people, each person's share will decrease by $2500. how many people have you found so far?
Thank you immensely,
Andrew
You can put this solution on YOUR website! 1) A car radiator contains 10 liters of a 30% solution.
How many liters will have to be replaced with pure antifreeze if the resulting
solution is to be 50% antifreeze?
:
let x = amt of pure antifreeze to be added
and also
let x = amt of 30% solution to be removed
:
.30(10-x) + x = .50(10)
:
3 - .3x + x = 5
:
-.3x + 1x = 5 - 3
:
.7x = 2
x =
x = 2.857 liters of 30% solution replaced by pure antifreeze
:
Check solution:
.30(10-2.857) + 2.857 = .50(10)
2.143 + 2.857 = 5
:
:
2) You are planning to start a business that will require an investment of $90,000.
You have found some people who are willing to share equally in the venture.
If you find three more people, each person's share will decrease by $2500.
how many people have you found so far?
:
Let x = no. of people so far:
then
(x+3) = no. of people to decrease share by $2500
:
Original share amt = Three more share amt + $2500 = + 2500
Multiply equation x(x+3); results
90000(x+3) = 90000x + 2500x(x+3)
:
90000x + 270000 = 90000x + 2500x^2 + 7500x
:
Arrange on the right:
0 = 90000x - 90000x + 2500x^2 + 7500x - 270000
:
A quadratic equation:
2500x^2 + 7500x - 270000 = 0
:
Simplify, divide by 2500
x^2 + 3x - 108 = 0
:
Factors to:
(x+12)(x-9) = 0
Positive solution
x = 9 people originally
:
:
Check solution:
90000/9 = 10000
90000/12 = 7500
----------------
difference 2500
