Mrs. boyd has a desk full of quarters and nickels. if she has a total of 26 coins with a total face value of $5.10, how many of the coins are quarters and how many are nickels?

19 quarters; 7 nickels

Work Shown:

q = number of quarters

n = number of nickels

q+n = 26 because we have 26 coins that are quarters or nickels. Solve for q to get q = 26-n (subtract n from both sides). This will be used in the second equation to replace every copy of 'q' with '26-n'

25*q is the total value of all the quarters, and this value is in cents. Similarly, 5n is the total value of all the nickels (value in cents). The total value of all the coins is 25q+5n which is equal to 510 (since 510 cents = $5.10)

25q+5n = 510

25(q)+5n = 510

25(26-n)+5n = 510 replace q with 26-n (see above)

25(26)-25(n)+5n = 510 ... distribute

650-25n+5n = 510

650-20n = 510

650-20n-650 = 510-650 ... subtract 650 from both sides

-20n = -140

-20n/(-20) = -140/(-20) ... divide both sides by -20

n = 7

There are 7 nickels

Use this to find q

q = 26-n

q = 26-7 replace n with 7

q = 19

and there are 19 quarters