Chapter 11, Problem 2MPS

To determine

To find: The amount of die added to increase the strength to $50\%$ .

Answer to Problem 2MPS

The amount of die added to increase the strength to $50\%$ is $480\text{g}$.

Explanation of Solution

Given information:

The amount of die solution chemist have is $800\text{g}$ .

The original; strength is $20\%$ .

The strength up to which the die is to be increased is $50\%$ .

Calculation:

Assume that the amount of die to be added is $x$ .

Calculate the amount of die in $800\text{g}$ solution.

  $\begin{array}{c}\text{actual die}=\left(800\text{g}\right)\left(\frac{20}{100}\right)\\ =160\text{g}\end{array}$

Total amount of die will be $x+160\text{g}$ .

Total amount of die solution will be $x+800$ .

Calculate the amount of die to be mixed to get $50\%$ strength.

  $\begin{array}{l}\frac{\left(160+x\right)}{\left(800+x\right)}=\frac{50}{100}\\ \frac{\left(160+x\right)}{\left(800+x\right)}=\frac{1}{2}\\ 2x-x=800-320\\ x=480\text{g}\end{array}$

Therefore, the amount of die added to increase the strength to $50\%$ is $480\text{g}$.