Chapter A.8, Problem 40AYU

To determine

To find: How much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution that is $60\%$ antifreeze?

Answer to Problem 40AYU

5 litres need to be drained and replaced with pure antifreeze.

Explanation of Solution

Given:

The cooling system of a certain foreign-made car has a capacity of 15 litres. If the system is filled with a mixture that is $40\%$ antifreeze.

Calculation:

Let $x=$ liters of mixture to be drained and replaced with pure antifreeze.

$0.4\left(15\right)=6$ litres of antifreeze in the system at beginning.

$0.4x=$ litres of antifreeze that will be removed by draining.

$6-0.4x=$ litres of antifreeze left in system after draining.

$6-0.4x+x=$ litres of antifreeze left in system after draining with pure antifreeze.

$\frac{6+0.6x}{15}=0.6$

$6+0.6x=9$

$0.6x=3$

Therefore $x=5$.

5 litres need to be drained and replaced with pure antifreeze.