Question

Paul has 12 coins in his pocket, consisting entirely of dimes and quarters. If he has a total of 195 cents in coins, how many coins of each type are in his pocket?

Answer 1

Let x be the number of dimes

and y be the number of quarters

Total number of coins = 12

So number of dimes + number of quarters = total number of coins

x + y = 12 ---------> equation 1

We know, 1 Quarter = 25 cents, 1 Dime = 10 cents, total cents = 196

y quarters = 25y cents , x dimes = 10x cents

x dimes + y quarters = 195 cents

10x + 25y = 195 -----------> equation 2

Now solve both equations

x + y =12, we solve for y by subtracting x on both sides

y = 12-x

Now substitute y in second equation

10x + 25(12-x) = 195

10x + 300 -25x = 195 (combine like terms)

-15x + 300 = 195 (subtract 300 on both sides)

-15x = -105 ( divide by -15)

x=7

y= 12-x

y=12-7 = 5

The number of dimes = 7

Number of quarters = 5