Math system of equations- coins

Question

John has 34 coins in nickels and dimes. The total value of the coins is $2.45. Use the system of equations to find how many nickels and dimes he has.

Answer 1

n is nickels. d is dimes.

n + d = 34

.05n + .10d = 2.45

Multiple the second equation by -10, then add to the first.

-.5n -1d = -24.50

n + d = 34

.5n = 9.50

n = 9.5/.5 = 95/5 = 19

19 + d =34

d = 34 -19 = 15

19 nickels and 15 dimes

Answer 2

Here's another way, using substitution:

n + d = 34, so n = 34 - d

0.05n + 0.10d = 2.45 Substitute for n in the equation:

0.05(34 - d) + 0.10d = 2.45. Use the distribution property: 1.70 - 0.05d + 0.10d = 2.45

1.70 + 0.05d = 2.45 Subtract 1.70 from both sides -> 0.05d = 2.45 - 1.70 -> 0.05d = 0.75

divide by 0.05 -> d = 0.75/0.05 = 15 dimes

n = 34 - 15 = 19 nickels