# Question 016ba

Sep 4, 2017

$\frac{3}{17}$ 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:

$\frac{1 \text{gallon}}{17} = \frac{x}{3}$

$x = \frac{1 \times 3}{17}$ gallons

$x = \frac{3}{17}$ of a gallon of water must be added.

Sep 4, 2017

Another approach just for the hell of it!

$\frac{3}{17}$ gallons $\approx 0.1765$ 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 $x = 1 \text{ gallon}$

Thus we have

$\frac{85}{100} x = 1$

$x = 1 \times \frac{100}{85} \text{ }$ this is water + antifreeze

so the amount of added water is:

$\frac{100}{85} - 1 \textcolor{w h i t e}{\text{ddd")->color(white)("ddd}} \frac{100}{85} - \frac{85}{85}$

$= \frac{15}{85} \textcolor{w h i t e}{\text{dddd")->color(white)("ddddd")(15-:5)/(85-:5)color(white)("ddd") =color(white)("d}} \frac{3}{17}$ of a gallon

$\approx 0.1765$ gallons to 4 decimal places