You have 12 coins. Some quarters and dimes. You have a total of $2.40, how many of each coin do you have?

Work Shown:

d = number of dimes

q = number of quarters

1 dime = 10 cents

d dimes = 10d cents

1 quarter = 25 cents

q quarters = 25q cents

d+q = 12 since we have 12 coins total

q = -d+12 after solving for q

10d+25q = total value in cents

10d+25q = 240

10d+25(-d+12) = 240 ... plug in q = -d+12

10d-25d+300 = 240

-15d+300 = 240

-15d = 240-300

-15d = -60

d = -60/(-15)

d = 4

q = -d+12

q = -4+12

q = 8

Since d = 4 and q = 8, this means we have 4 dimes and 8 quarters

Check:

4 dimes = 4*10 = 40 cents

8 quarters = 8*25 = 200 cents

(4 dimes) + (8 quarters) = (40 cents) + (200 cents) = 240 cents

240 cents = 240/100 = $2.40

We have 4+8 = 12 coins total

The answers are confirmed