Question 173632
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