Question 1006173: You have two types of coins in your pockets. If you have 18 coins in total and they add up to $3.30, what are the two types of coins? (e.g. Pennies, nickels, dimes, quarters, half-dollars, dollar coins)?
I worked the beginning of the problem like this:
x+x*(18-x)=330
x+18x-x^2=330
x^2-18x+330=0
(x-12)(x-6)=0
x+6 and x=12
I know there are 12 quarters and 6 nickels. However, I just don't know how to set up the equation that would show you what type of coins they are. Please help.
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website!
Let's do some dividing. 330 by the number of cents in
the various coins:
330/100 = 3.3
330/50 = 6.6
330/25 = 13.2
330/10 = 33
330/5 = 66
330/1 = 330
To have 18 coins, since 13.2 is closest to 18, one of the coin types
has to be quarters.
Hey! 13 quarters is $3.25 and 5 more cents is 18 coins and that's $3.30.
So there's a solution you didn't have.
Try 1 less quarter, that's 12 quarters or $3. Can we make the
remaining 30 cents with 6 of the same kind of coin? Yes 6 nickels!
That's the solution you have.
Try 1 less quarter, that's 11 quarters or $2.75. Can we make the
remaining 55 cents with 7 of the same kind of coin? Nope!
Try 1 less quarter. That's 10 quarters or $2.50. Can we make the
remaining 80 cents with 8 of the same kind of coin? Yes, 8 dimes!
That's another solution you didn't have.
No use to try for 9 quarters. That's $2.25/ leaving $1.05, No way
to have 9 of the same kind of coin totaling that.
So there are three solutions
10 quarters and 8 dimes.
12 quarters and 6 nickels.
13 quarters and 5 pennies.
Edwin
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