Percent with Money

Question

The amount of money that Henry and Frank have is in the ratio of $6 : 5$. After he spent $50%$ of his money, Henry had $\$68$ less than Frank. How much did Henry have left?

Answer 1

Call the initial amounts of money $h$ (for Henry) and $f$ (for Frank). We know that:

$$6f = 5h$$ $$h-(50\%)h = f - 68$$

In other words:

$$f = \frac{5}{6}h$$ $$\frac{1}{2}h = f - 68$$

Substituting the first expression in the second gives:

$$\frac{1}{2}h = \frac{5}{6}h - 68$$

which becomes

$$-\frac{1}{3}h = - 68$$

so

$$h = 204$$

and the amount he has left at the end is half of that, so 102$.