Question

Question #016ba

Answer 1

`3/17` of a gallon of water

Explanation:

A solution that is `85%` antifreeze means it is in the ratio:

Antifreeze : water

`85% : 15%" "larr` this simplifies to

`17:3`

Use direct proportion:

`(1 "gallon")/(17) = x/(3)`

`x = (1 xx 3)/17` gallons

`x = 3/17` of a gallon of water must be added.

Answer 2

Another approach just for the hell of it!

`3/17` gallons `~~0.1765` gallons to 4 decimal places

Explanation:

We know that we are going to use all of the 1 gallon of antifreeze.

The target concentration is 85%

Let the final volume of the blend be `x`

Then 85% of `x = 1" gallon"`

Thus we have

`85/100x=1`

`x=1xx100/85" "` this is water + antifreeze

so the amount of added water is:

`100/85 - 1color(white)("ddd")->color(white)("ddd")100/85-85/85`

`=15/85color(white)("dddd")->color(white)("ddddd")(15-:5)/(85-:5)color(white)("ddd") =color(white)("d") 3/17` of a gallon

`~~0.1765` gallons to 4 decimal places