# The amount of coolant drain and replace with water to reduce the antifreeze concentration.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.6, Problem 57E
To determine

## To find: The amount of coolant drain and replace with water to reduce the antifreeze concentration.

Expert Solution

The amount of coolant drain and replace with water is 0.6 liters.

### Explanation of Solution

Given:

A car radiator is filled with 60% antifreeze and 40% water.

The capacity of radiator is 3.6 L.

The manufacturer suggests that optimal cooling of engine should be obtained with 50% antifreeze.

Calculation:

Let the amount of coolant drain and replace with water be x.

Tabulate the given information into the language of algebra.

 In words In Algebra Amount of coolant drain and water add x Antifreeze remaining in tank 0.6(3.6−x) Water remaining in tank 0.4(3.6−x) Total water x+0.4(3.6−x)

Model the equation for the above information.

(Antifreezeremainingintank)=(Antifreezeamountintank)(Antifreezeremainingintank+Totalwater)0.6(3.6x)=0.50[0.6(3.6x)+x+0.4(3.6x)]

Simplify the above equation for x,

2.160.6x=0.50(2.160.6x+x+1.440.4x)2.160.6x=0.50(3.6)2.160.6x=1.8

Further simplify the above equation.

0.6x=0.36x=0.6

Thus, the amount of coolant drain and replace with water is 0.6 liters.

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