Maria has $13.60 in dimes and quarters. She has 34 coins. How many dimes could she possibly have?

Answer 1

Using d for number of dimes and q for number of quarters, you have two simultaneous equations:

d + q = 34 (34 coins total)
0.10d + 0.25q = 13.60 (value= $13.60)

Place the first equation in terms of q:

d + q = 34
q = 34 - d

And then substitute into the second one:

0.10d + 0.25q = 13.60
0.10d + 0.25(34-d) = 13.60
0.10d + 8.5 - 0.25d = 13.60
-0.15d = 5.10
d = -34

That's clearly incorrect, you can't have negative 34 dimes.

However, on checking, even if all 34 coins were quarters, they'd only be worth $8.50 ($0.25 * 34 = $8.50). Changing coins from quarters to dimes reduces the total... so it is not possible to have $13.60 with 34 coins which are all dimes or quarters.

Are you sure the problem was stated correctly?

Answer 2

Theres no way she could have 13.60 because even if she had all quarters, she would only have $8.50.

Answer 3

There is an error in your question. Please check it!