Question

1. Jack and Betty have 40 coins that are nickels and dimes. If the value of

the coins is $3.15, how many of each type of coin do they have?

Answer 1

Number of nickels = 17

Number of dimes = 23

Explanation:

Let

x = number of nickels

y = number of dimes

x + y = 40 (1)

0.05x + 0.10y = 3.15 (2)

From (1)

x = 40 - y

Substitute x = 40 - y into (2)

0.05x + 0.10y = 3.15 (2)

0.05(40 - y) + 0.10y = 3.15

2 - 0.05y + 0.10y = 3.15

- 0.05y + 0.10y = 3.15 - 2

0.05y = 1.15

y = 1.15/0.05

y = 23

Substitute y = 23 into (1)

x + y = 40 (1)

x + 23 = 40

x = 40 - 23

x = 17

Number of nickels = 17

Number of dimes = 23