Answer:
There are 16 nickels and 15 dimes.
Explanation:
let x = number of dimes
let y = number of nickels
x + y = 31
.1x + .05y = 2.30
Solve x + y = 31 for x
x = 31 - y
multiple the second equation by 100 to eliminate the decimals.
10x + 5y = 230 Substitute 31 - y for x
10(31-y) + 5y = 230 Distribute the 10
310 -10y + 5y = 230 Combine like terms
310 -5y = 230 Subtract 310 from both sides
-5y = -80 Divide both sides by -5
y = 16
There are 16 nickels.
Plug in 16 for y to solve for x
x + y = 31
x + 16 = 31 Subtract 16 from both sides
x = 15
There are 15 times.
Check:
10x + 5y = 230
10(15) + 5(16) = 230
150 + 80 = 230
230 = 230