Cynthia has a cup full of dimes and quarters that she would like to put in her savings account. When she takes the cup to the bank, the banker tells Cynthia that the 386 coins in the cup are worth $58.10. How many quarters does Cynthia have in her cup?

A.

126

B.

130

C.

256

D.

386

Let d and q be the number of dimes and quarters respectively.

We are told that there are 386 coins in total.

d+q=386 solve this for d (because we are only looking for the number of quarters in the final solution ...)

d=386-q

We are also told that the coins have a value of $58.10 which is equal to 5810 cents. Each quarter is worth 25 cents and each dime is worth 10 cents. So we can say:

25q+10d=5810, now using d found above in this equation gives you:

25q+10 (386-q) = 5810 perform indicated multiplication on left side

25q+3860-10q=5810 combine like terms on left side

15q+3860=5810 subtract 3860 from both sides

15q=1950 divide both sides by 15

q=130

So there are 130 quarters in Cynthia's cup.