Financial Word Problem Setup.

Question

A person spends one-third of his income, saves one-fourth, and pays away $5$ percent on the whole as interest at $7\frac{1}{2}$ percent on debts previously incurred, and then has $110$ pounds remaining: What was the amount of his debts?

I don't quite understand some of the wording in this problem:

1. ...saves one-fourth...

Saves one-fourth of his whole income or just the $\frac{2}{3}$ he has left? I'm not quite certain.

2. ..., and pays away 5 percent on the whole as $7\frac{1}{2}$ percent on debts previously incurred, ...

So he just pays $7\frac{1}{2}$ percent on the 5 percent of the whole or he pays $7\frac{1}{2}$ percent on the 5 percent of the whole plus everything else that he had payed before that.

I'm not very good at word problems, so bear with me. Ask me any questions regarding my confusion or the problem. As a side note, the answer to this problem is apparently 200 pounds (which I'm still unable to obtain).

Thanks.

Answer 1

Suppose the income is $\$x$.

The word ‘on the whole’ indicates that he spent $\frac x3$, $\frac x4$, and $0.05x$.

Let the debt be $\$d$. Then $$0.05x=0.075d$$

He also has $$x=\frac x3 +\frac x4 +0.05x +110$$

The rest should be fine.

Answer 2

Let total income be $x$. The person spends $x/3$, saves $x/4$, and payes $0.05x$ in interest, which means he has $x - x/3 - x/4 - 0.05x$ left. You should be able to get to the answer from here.