Question

Sofia has 25 coins in nickels and dimes in her pocket for a total of $1.65. How many of each type of coin does she have? First complete the equations below, where N stands for nickels and D stands for dimes. [?]N + [ ]D = 1.65; N + D ​

Answer 1

Answer: There are 8 dimes and 17 nickels.

Step-by-step explanation: 0.05N+.10D=1.65; N+D=25

Answer 2

Explanation:

Let n represent nickels & d dimes

given: n + d = 25 #1 (number of coins)

given: .05n + .10d = 1.65 #2 (amount in dollars)

n = 25 - d #3 (rewrite of #1)

.05(25 -d) + .10d = 1.65 (substitute #3 in #2)

1.25 - .05d + .10d = 1.65 (multiply out the left side)

.05d = .40 (collection of like terms)

d = 8 (divided both sides by.05)

n + 8 = 25 (substitute answer for d in #1)

n = 17 (subtract both sides by 8)

There are 8 dimes and 17 nickels.

Check:

17(.05) + 8(.10) = 1.65 (answers in #2)

.85 + .80 = 1.65 (multiply out the left side)

1.65 = 1.65 ✔️ QED