Chapter A.8, Problem 59AYU

To determine

To find: Go through an algebraic solution. What happens?

Answer to Problem 59AYU

No amounts of $25\%$ and $48\%$ solutions will give a $58\%$ solution.

Explanation of Solution

Given:

Without solving, explain what is wrong with the following mixture problem: How many litres of $25\%$ ethanol should be added to $\text{20}$ litres of $48\%$ ethanol to obtain a solution of $58\%$ ethanol?

Calculation:

$0.25x +0.48*20=0.58\left(x+20\right)$

$25x+48*20=58x+58x*20$

$-23x=10*20$

$x=\frac{-200}{23}$ (amount of $25\%$ solution: meaningless).