Question 748298
Let q represent the number of quarters and d represent the number of dimes.
Since there are 24 coins:

{{{q+d=24}}}

Let's solve this for one of the variables, I'll choose q.  So subtract d from both sides:

{{{q=24-d}}}



Since quarters are worth .25 and dimes are worth .10, we have another equation:

{{{.25q+.1d=4.35}}}

Now, we can use the equation we found earlier (q=24-d) and plug in 24-d for q:

{{{.25q+.1d=4.35}}}

{{{.25(24-d)+.1d=4.35}}}

Now distribute and combine like terms:

{{{6-.25d+.1d=4.35}}} 

{{{6-.15d=4.35}}}

Subtract 6 from both sides:

{{{-.15d = -1.65}}}

Divide both sides by -.15:

{{{d=11}}}

Thus, there are 11 dimes.  
We found that q=24-d, so:

{{{q=24-11}}}

{{{q=13}}}

There are 13 quarters and 11 dimes.