Question 620082: Please Help i'd greatly appreciate it!
Bob has a coin jar containing nickels, quarters, and one dollar coins. He has a total of 44 coins totaling $9.75. And, he has five times as many nickels as he has one dollar coins. How many of each coin does he have?
Write a system of equations that can be used to solve this problem. Define what your variables represent. (Nickel $.05, Quarter $.25)
Thanks you!
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Bob has a coin jar containing nickels, quarters, and one dollar coins. He has a total of 44 coins totaling $9.75. And, he has five times as many nickels as he has one dollar coins. How many of each coin does he have?
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Quantity Eq::: n + q + d = 44 coins
Value Eq::::: 5n +25q +100d= 975 cents
Quantity Eq:: n + 0 - 5d = 0
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Solve the system anyway you can to get:
n = 25
q = 14
d = 5
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Cheers,
Stan H.
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Answer by Edwin McCravy(20065)  (Show Source):
You can put this solution on YOUR website! Please Help i'd greatly appreciate it!
Bob has a coin jar containing nickels, quarters, and one dollar coins. He has a total of 44 coins totaling $9.75. And, he has five times as many nickels as he has one dollar coins. How many of each coin does he have?
Write a system of equations that can be used to solve this problem. Define what your variables represent. (Nickel $.05, Quarter $.25)
Thanks you!
Let the number of dollar coins be D
>>...he has five times as many nickels as he has one dollar coins...<<
So the number of nickels is 5D
Let Q = the number of quarters.
>>...He has a total of 44 coins...<<
Therefore
D + 5D + Q = 44 or
6D + Q = 44
>>...totaling $9.75...<<
So
1.00D + .25Q + .05(5D) = 9.75 or
1.00D + .25Q + .25D = 9.75 or multiplying through by 100,
100D + 25Q + 25D = 975 or combining like terms
125D + 25Q = 975 or dividing through by 25
5D + Q = 39
So we have this system of equations:
6D + Q = 44
5D + Q = 39
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Solve that system and get D=5, Q=14
So there are 5 dollar coins, 14 quarters, and since the number
of nickels is 5D, that's 5(5) or 25 nickels.
Edwin
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