Chapter 9.5, Problem 14P

To determine

To find:The amount of dye to be added to increase the strength to 50%.

Answer to Problem 14P

The amount of dye to be added to increase the strength to 50%is $480\text{ gram}$ .

Explanation of Solution

Given information: The 800 gram dye has the 20% strength of origin.

Calculation:

Assume the amount of dye added is $x$ .

The amount of solution becomes $800+x$ . Since the strength should be 50% then the amount must be $0.5\left(800+x\right)$ .

The amount in dilute solution is $0.2\left(800\right)=160$ .

The dye in new solution is $160+x$ .

Equate the amount of dye in new and existing solution.

$\begin{array}{l}0.5\left(800+x\right)=160+x\\ 400+0.5x=160+x\\ x=480\text{ gram}\end{array}$

Thus, the amount of dye to be added to increase the strength to 50% is $480\text{ gram}$ .