Question 779727: I have $5.50 total in my pocket, consisting of nickels, dimes and quarters. There are 30 coins total. There are also, 2 times as many dimes as nickels. How many of each coin do I have in my pocket?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! I have $5.50 total in my pocket, consisting of nickels, dimes and quarters. There are 30 coins total. There are also, 2 times as many dimes as nickels. How many of each coin do I have in my pocket?
>>There are 30 coins total.<<
n + d + q = 30
>>I have $5.50 total...<<
$0.05n + $0.10d + $0.25q = $5.50
5n + 10d + 25q = 550
>>...2 times as many dimes as nickels...<<
d = 2n
n + d + q = 30
5n + 10d + 25q = 550
Substitute 2n for d in both of those:
n + 2n + q = 30
3n + q = 30
5n + 10(2n) + 25q = 550
5n + 20n + 25q = 550
25n + 25q = 550
Divide through by 25
n + q = 22
Solve for q:
q = 22 - n
Substitute in
3n + q = 30
3n + (22 - n) = 30
3n + 22 - n = 30
2n + 22 = 30
2n = 8
n = 4
Substitute in
q = 22 - n
q = 22 - 4
q = 18
Substitute in
d = 2n
d = 2(4)
d = 8
Answer:
18 quarters = 18×$0.25 = $4.50
8 dimes = 8×$0.10 = 0.80
4 nickels = 4×$0.05 = 0.20
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30 coins value = %5.50
Edwin
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