Question

You have 37 coins that are nickels, dimes, and pennies. The total value of the coins is $1.55. There are twice as many pennies as dimes. Find the number of each type of coin in the bank.

Answer: Let n be the number of nickel


s, d be the number of dimes, and p be the number of pennies.

Answer 1

n = number of nickels = 7

d = number of dimes = 10

p = number of pennies = 20

Explanation:

Let

n = number of nickels

d = number of dimes

p = number of pennies.

n + d + p = 37

0.05n + 0.10d + 0.01p = 1.55

p = 2d

Substitute p = 2d into the equation

n + d + 2d = 37

0.05n + 0.10d + 0.01(2d) = 1.55

n + 3d = 37

0.05n + 0.10d + 0.02d = 1.55

n + 3d = 37 (1)

0.05n + 0.12d = 1.55 (2)

Multiply (1) by 0.05

0.05n + 0.15d = 1.85

0.05n + 0.12p = 1.55

Subtract

0.15d - 0.12d = 1.85 - 1.55

0.03d = 0.3

d = 0.3/0.03

= 10

d = 10

p = 2d

= 2(10)

p = 20

n + d + p = 37

n + 10 + 20 = 37

n + 30 = 37

n = 37 - 30

n = 7

n = number of nickels = 7

d = number of dimes = 10

p = number of pennies = 20