The capacity of a car radiator is 18 quarts. If it is full of a 20% antifreeze solution, how many quarts must be drained and replaced with a 100% solution to give 18 quarts of a 39% solution?

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Jadarosborough Jadarosborough · Answer 1 · 2016-01-09T03:58:54+01:00

.2(18-x)+x=.39(18)
x=4.275 quarts should be drained and replaced with pure antifreeze.

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PratikshaS PratikshaS · Answer 2 · 2022-06-15T07:26:35+02:00

4.275 quarts must be drained and replaced with a pure antifreeze.

"It is a ratio that can be expressed as a fraction of 100."

For given example,

Let 'x' be the number of quarts that must be drained and replaced with a 100% solution.

The capacity of a car radiator is 18 quarts.

It is full of a 20% antifreeze solution.

So, the amount of mixture drained is,

20 percent of (18 - x)

⇒ (18 - x) × (20/100) = 0.20(18 - x)

18 quarts of a 39% solution

The value of 39 percent of 18 is,

⇒ 18 × (39/100) = 18 × 0.39

Th amount of solution drained and replaced with a 100% solution to give 18 quarts of a 39% solution.

⇒ 0.20(18 - x) + x = 18 × 0.39

⇒ 3.6 - (0.20)x + x= 7.02

⇒ (-0.20+1)x = 7.02 - 3.6

⇒ 0.8x = 3.42

⇒ x = 4.275 quarts

Therefore, 4.275 quarts must be drained and replaced with a pure antifreeze.

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