SOLUTION: Please help me solve this problem: Luis told his sister Rosi "If you can guess the amount of money in my piggy bank, you can have it. The bank contains only dimes and quarters. Th

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Question 173632: Please help me solve this problem:
Luis told his sister Rosi "If you can guess the amount of money in my piggy bank, you can have it. The bank contains only dimes and quarters. There are no more than 8 quarters and no more than 4 dimes. I have at least ten coins in all." Write a system of inequalitites for this situation.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
let d = number of dimes
let q = number of quarters
formulas to work with:
d <= 4
q <= 8
d+q >= 10
1 dime is worth 10 cents = .10d
1 quarter is worth 25 cents = .25q
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you can't solve this for the exact amount of money but you can solve this for a range of values that will contain the exact amount of money.
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since the total number of coins has to be greater than or equal to 10, you start with 10 coins and work your way up.
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working within the constrictions, here's how it will go.
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10 coins:
8q + 2d = $2.20
7q + 3d = $2.05
6q + 4d = $1.90
that's all that's possible since you can't have more than 8 quarters and you can't have more than 4 dimes.
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11 coins:
8q + 3d = $2.30
7q + 4d = $2.15
that's all that's possible since you can't have more than 8 quarters and you can't have more than 4 dimes.
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12 coins:
8q = 4d = $2.40
that's all that's possible since you can't have more than 8 quarters and you can't have more than 4 dimes.
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anything above 12 coins is not possible since you would require more than 8 quarters or more than 4 dimes.
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your possible options for the amount of money in the bank are:
8q + 2d = $2.20
7q + 3d = $2.05
6q + 4d = $1.90
8q + 3d = $2.30
7q + 4d = $2.15
8q = 4d = $2.40