Word problem! Need help!

Question

Emily has nickels, dimes, and quarters in her piggy bank. She has twice as many dimes as nickels and 12 fewer quarters than dimes. The total value of the coins is $9.00. How many of each coin type does Emily have?

Answer 1

Hello Naomi,

From the second sentence, we can get the following two equations:

D = 2N {Equation 1} and

Q = D - 12 {Equation 2}

From the third sentence, we have:

.05N + .10D + .25Q = 9.00

→ 5N + 10D + 25Q = 900 by multiplying through by 100 {to clear the decimals}

→ N + 2D + 5Q = 180 by dividing through by 5 {why...because I can! :-) }

→ 2N + 4D + 10Q = 360 multiplying through by 2 {so that I can swap out 2N for D using Equation 1}

→ D + 4D + 10(D - 12) = 360

→ D + 4D + 10D - 120 = 360

→ 15D = 480

→ D = 32

→ N = 16

→ Q = 20

Thank you for posting the question with Wyzant.

Michael E.

Answer 2

D = 2n

Q = D - 12 = 2n - 12

10(2n) + 25(2n-12) + 5n = 900

20n + 50n - 300 + 5n = 900

75n - 300 = 900

75n = 1200

n = 16

16 nickels ---> 80 cents = $0.80

32 dimes ----> 320 cents = $3.20

20 quarters ---> 500 cents = $5