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
