Question

Sal has quarters, dimes and nickels. She has 52 coins total. She has 3 more quarters than dimes and 5 fewer nickels than nickels. How many dimes does she have?

Answer 1

Depending upon a correction to the question:
the intended answer was probably `18` dimes

Explanation:

Let
`color(white)("XXX")Q` represent the number of quarters;
`color(white)("XXX")D` represent the number of dimes; and
`color(white)("XXX")N` represent the number of nickels.
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Option 1: line should have read: 5 fewer dimes than nickels.

We are told
[1]`color(white)("XXX")Q+D+N=52`
[2]`color(white)("XXX")Q=D+3`
[3]`color(white)("XXX")D=N-5`

`D=N-5 color(white)("XX")rarrcolor(white)("XX")N=D+5`

So we can substitute `D+3` for `Q` and `D+5` for `N` in [1]

`color(white)("XXX")(D+3)+D+(D+5)=52`

`color(white)("XXX")3D+8=52`

`color(white)("XXX")3D=44`

`color(white)("XXX")D=14 2/3`
(since this isn't likely, let's reject Option 1)
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Option 2: line should have read: 5 fewer nickels than dimes.

We are told
[1]`color(white)("XXX")Q+D+N=52`
[2]`color(white)("XXX")Q=D+3`
[3]`color(white)("XXX")N=D-5`

So we can substitute `D+3` for `Q` and `D-5` for `N` in [1]

`color(white)("XXX")(D+3)+D+(D-5)=52`

`color(white)("XXX")3D-2=52`

`color(white)("XXX")3D=54`

`color(white)("XXX")D=18`

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Of course it is possible that one of the "nickels" in
`color(white)("XXX")`...5 fewer nickels than nickels
should have been "quarters"... but let's quit while we have a reasonable answer.