Alex has 84 quarters and nickels worth a total of $17.80.

Which equation can be used to find q, the number of quarters Alex has?

A. 0.25q + 0.05 (q - 84) = 17.80

B. 0.05q + 0.25 (84 - q) = 17.80

C. 0.25 (q - 84) + 0.05q = 17.80

D. 0.05 (84 - q) + 0.25q = 17.80

The value of the coin times the number of coins, summed up, equals the total value

the value of a quarter is $0.25

and quarters can be represented as a q

the value of nickels are $0.05

and can be represented with an n

there are 84 quarters and nickels in total

so

q + n = 84

which have a total value of $17.80

so

0.25q + 0.05n = 17.80

the q + n = 84 can be rearranged by subtracting q from both sides

n = 84 - q

then we can plug that into the 0.25q + 0.05n = 17.80 equation

and get

0.25q + 0.05 (84 - q) = 17.80

or

0.05 (84 - q) + 0.25 = 17.80

therefore your answer is D.