I have a handful of coins which are quarters and dimes there is a total of 26 coins, the total amount = $5.15. I am trying to figure out how to write an equation to figure out how many quarters and dimes i have

D+q=26, so we can say d=26-q

Then we are told:

.1d+.25q=5.15, using d found above makes this equation become:

.1 (26-q) +.25q=5.15 perform indicated multiplication on left side

2.6-.1q+.25q=5.15 combine like terms on left side

2.6+.15q=5.15 subtract 2.6 from both sides

.15q=2.55 divide both sides by. 15

q=17, and since d=26-q

d=26-17

d=9

So there are 9 dimes and 17 quarters.