SOLUTION: 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

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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?
----
Quantity Eq::: n + q + d = 44 coins
Value Eq::::: 5n +25q +100d= 975 cents
Quantity Eq:: n + 0 - 5d = 0
-----------------------
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
--------------

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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