- #1

musicgold

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- 19

- Homework Statement
- Given 8 dimes (10 ¢ coins) and 3 quarters (25 ¢ coins), how many different amounts

of money can be created using one or more of the 11 coins?

- Relevant Equations
- m = 10d + 25q , where 0 <= d < 9 and 0 <= q < 4

where d is number of dimes and q is number of quarters used to get a m.

While I found 26 possible values of m with the trial and error method, I wanted to find an elegant approach to solve such problems.

I think the following equation represents the problem:

where d is the number of dimes and q is number of quarters used to get a m.

As d can take 9 values and q can take 4 values, m can take 36 possible values, some of which will be duplicate. Note that the combination d=0, q= 0 is invalid.

I am not able to find a way to quickly isolate the potential duplicate values.

When d =5, m can have 4 values 50, 75, 100 and 125 cents. 50 and 75 will also be created with only 2 or 3 quarters. So I have found 2 duplicates, and 1 invalid amounts out of 10.

How should I move forward from here?

Thanks

I think the following equation represents the problem:

**m = 10d + 25q**where ## 0 <= d < 9 ## and ## 0 <= q < 4 ##where d is the number of dimes and q is number of quarters used to get a m.

As d can take 9 values and q can take 4 values, m can take 36 possible values, some of which will be duplicate. Note that the combination d=0, q= 0 is invalid.

I am not able to find a way to quickly isolate the potential duplicate values.

When d =5, m can have 4 values 50, 75, 100 and 125 cents. 50 and 75 will also be created with only 2 or 3 quarters. So I have found 2 duplicates, and 1 invalid amounts out of 10.

How should I move forward from here?

Thanks