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There must be at least one nickel, to account for the 5 cents of the 75 cents.

So, one solution would be 1 nickel and 277 dimes.

This would be (277 x 0.10) + 0.05 = 27.70 + 0.05 = 27.75

Another solution would be 1 dime and 553 nickels.

This would be (553 x 0.05) + 0.10 = 27.65 + 0.10 = 27.75

You will have an odd number of nickels in an solution. Possible solutions include

1 nickel & 277 dimes

3 nickels & 276 dimes

5 nickels & 275 dimes

7 nickels & 274 dimes

9 nickels & 273 dimes

up to

553 nickels and 1 dime

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Q: How do you show 2 different possible combinations of dimes and nickels that would total 27.75?
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