Chapter 9.6, Problem 3CYP

To determine

To find : how much of the $65\%$ fruit juice solution must be added to create a fruit punch that is $35\%$ fruit juice

Answer to Problem 3CYP

  $65\%$ Fruit juice solution must be added to create $\text{52}\text{.5 milliliters}$ of a fruit punch that is $35\%$ fruit juice.

Explanation of Solution

Given information :

Jimmy adds a $65\%$ fruit juice solution to 15 milliliters of a drink that is $10\%$ fruit juice

Calculation :

  $10\%$ Fruit juice in a drink $=15\text{ milliliters}$

  $1\%$ Fruit juice in a drink $=\frac{15}{10\%}\text{milliliters}$

  $35\%$ Fruit juice in a drink

  $\begin{array}{l}=\frac{15}{10\%}\cdot \text{35\% milliliters}\\ \text{=}\frac{15\cdot 35\cdot 100}{10\cdot 100}\\ =\frac{15\cdot 7}{2}\\ =\frac{105}{2}\\ =52.5\text{ milliliters}\end{array}$

Hence, $65\%$ Fruit juice solution must be added to create $\text{52}\text{.5 milliliters}$ of a fruit punch that is $35\%$ fruit juice.