1. ## Word problem.

The coin box of a gum vending machine, which accepts only dimes and quarters, contains $5.20. If the number of quarters is four more than the number of dimes, how many quarters are in the box? How do I use the above information to write out an equation and solve it??? 2. Originally Posted by Ash The coin box of a gum vending machine, which accepts only dimes and quarters, contains$5.20. If the number of quarters is four more than the number of dimes, how many quarters are in the box?

How do I use the above information to write out an equation and solve it???
Call q the number of quarters and d the number of dimes.

Then we know that
$\displaystyle 0.25q + 0.10d = 5.20$

$\displaystyle q = d + 4$

Subbing the second equation into the first:
$\displaystyle 0.25(d + 4) + 0.10d = 5.20$

$\displaystyle 0.25d + 1 + 0.10d = 5.20$

$\displaystyle 0.35d = 4.20$

$\displaystyle d = \frac{4.20}{0.35} = 12$

Thus q = 16. (Check: $\displaystyle 0.25 \cdot 16 + 0.10 \cdot 12 = 5.20$. Check!)

-Dan