Concept explainers
Mixture Problem The radiator in a car is filled with a solution of 60% antifreeze and 40% water. The manufacturer of the antifreeze suggests that for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.6 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level?
To find: The amount of coolant drain and replace with water to reduce the antifreeze concentration.
Answer to Problem 57E
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 |
|
Water remaining in tank |
|
Total water |
|
Model the equation for the above information.
Simplify the above equation for x,
Further simplify the above equation.
Thus, the amount of coolant drain and replace with water is 0.6 liters.
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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