SOLUTION: A coin bank contains only pennies, dimes, and quarters. The value of the coins is $4.49. There are 5 more pennies than quarters. The number of dimes is 1.5 times the number of penn
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Question 92622: A coin bank contains only pennies, dimes, and quarters. The value of the coins is $4.49. There are 5 more pennies than quarters. The number of dimes is 1.5 times the number of pennies. Find the number of each coin in the bank.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each sentence:
:
A coin bank contains only pennies (c), dimes (d), and quarters (q).
:
"The value of the coins is $4.49."
.01c + .10d + .25q = 4.49
:
"There are 5 more pennies than quarters."
q = c - 5; get everything in terms of c
:
"The number of dimes is 1.5 times the number of pennies."
d = 1.5c
:
Find the number of each coin in the bank.
.01c + .10d + .25q = 4.49
:
Substitute (1.5p) for d and (p-5) for q:
.01c + .10(1.5c) + .25(c-5) = 4.49
:
.01c + .15c + .25c - 1.25 = 4.49
:
.41c = 4.49 + 1.25
:
.41c = 5.74
:
c = 5.74/.41
:
c = 14 pennies
:
Find d:
d = 1.5(14)
d = 21 dimes
:
Find q:
q = 14 - 5
q = 9 quarters
:
:
Check: .01(14) + .10(21) + .25(9)
.14 + 2.10 + 2.25 = 4.49
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