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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?

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    The original question said 50%, not 50. – 2017-01-12
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    This is not a "Do my homework for me" site. If you don't say something about where this problem comes from, and what your own thoughts on how to solve it are, it will probably get closed. – 2017-01-12

1 Answers 1

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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$.