SOLUTION: In Poncho's Piggy bank there is $27.50 in nickels, dimes and quarters. He has 10 less nickels than quarters and half as many dimes as quarters. how many of each coin does he have?

Question 1102328: In Poncho's Piggy bank there is $27.50 in nickels, dimes and quarters. He has 10 less nickels than quarters and half as many dimes as quarters. how many of each coin does he have?
Answer by Lightning_Fast(78) (Show Source): You can put this solution on YOUR website!
We don't know how many quarters there are, so will represent how many quarters there are.
How many nickels are there? There are 10 less nickels than quarters, which can be represented by the following. The following means that for there to be the same number of nickels and quarters, the number of nickels must be increased by 10.

What about dimes? Well there are half as many dimes as quarters. For there to be as many dimes as quarters, the number of dimes must be multiplied by 2. So we get the following.

Now we know the equations of quarters, nickels, and dimes. These nickels, quarters, and dimes all add up to $27.50. This means the following.

Now we just plug in the equations we have above (isolating for N and D respectively) to get the following.
= 27.5}}}
Simplify and get the following.

Now we know the number of quarters, we can plug back in Q for the previous equations to obtain the following.

Doing the same for dimes, we get.

So in your final answer, there are 40 dimes, 70 nickels, and finally, 80 quarters that add up to the total of $27.50.
Hope I could help, Edwin.
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