SOLUTION: The cooling system of a car has a capacity of 15 liters. If the system currently has a mixture of 40% antifreeze how much of this mixture should be drained and replaced with pure

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Question 159080This question is from textbook Intermediate Algebra
: The cooling system of a car has a capacity of 15 liters. If the system currently has a mixture of 40% antifreeze how much of this mixture should be drained and replaced with pure antifreeze so that the system is filled with 50% antifreeze?
I think that the answer is 1.5 liters. I just don't know how to get it in an Algebraic expression. I used the equation 15(.5)=15(.4)+ a
Let a=the amount of antifreeze to be added. In case you couldn't tell I am severely confused.










0
This question is from textbook Intermediate Algebra

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
*See this one, thank you.
Let a, amount in Liters to be drained
b, amount of 100% A/F to be added
Therefore,
highlight%2815%280.40%29-a%280.40%29%2Bb%281.00%29=15%280.50%29%29 ------> working eqn
The above eqn means the 15L capacity with 40% A/F is drained with a liters amount with the same mixture of %40 A/F of course.Then you're adding 100% A/F in b liters amount that will result to the same capacity of 15L with 50% A/F
Also, take note:
15L-a%28L%29%2Bb%28L%29=15L
The cooling system 15L has taken out a%28liters%29 amount plus b%28liters%29 amount equals the same capacity of 15L
.

Continuing,

cross%2815L%29-a%28L%29%2Bb%28L%29=cross%2815L%29

a%28L%29=b%28L%29 ---> substitute in working eqn:

15%280.40%29-a%280.40%29%2Bhighlight%28a%29%281.00%29=15%280.50%29

6%2B0.60a=7.5

0.60a=7.5-6=1.5

cross%280.60%29a%2Fcross%280.60%29=cross%281.5%292.5%2Fcross%280.60%29

highlight%28a=2.5L%29 --------> amount to be drained = amount to be added

In doubt? go back working eqn:

15%280.40%29-2.5%280.40%29%2B2.5%280.40%29=15%280.50%29

6-1%2B2.5=7.5

7.5=7.5

thank you,

Jojo