SOLUTION: Lucy has acollection of 300 coins of 5 cents and ten cents coins. If the total value of her collection is 45.00, how many of each kind are there?

Question 330450: Lucy has acollection of 300 coins of 5 cents and ten cents coins. If the total value of her collection is 45.00, how many of each kind are there?
Answer by neatmath(302) (Show Source): You can put this solution on YOUR website!

Lucy has acollection of 300 coins of 5 cents and ten cents coins. If the total value of her collection is 45.00, how many of each kind are there?

This problem as written has no "real" answer.

If you had 300 10 cent coins with no 5 cent coins, that would only add up to 30 dollars. But the question says that the total value of the 300 coins is 45.00.

This is an impossible real world situation. Please check the question and submit again. :)

But if we go through the motions, this is what we are looking at:

Let x=number of 5 cent coins
Let y=number of 10 cent coins

Thus

x+y=300 given
.05*x+.10*y=45.00 given

We need to solve this system of equations!

Multiply the bottom equation by 20. Then we have:

x+y=300
x+2y=900

Then subtract the bottom equation from the top.

-y=-600 or y=600

Then x+y=300 or x-600=300 and x=-300

The only answer to this system of equations would be x=-300, y=600

Unfortunately, in real world terms, it is not possible to have a negative amount of coins!
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