Acollection of dimes and quarters is worth $6.50. there are 35 coins in all. how many dimes are there?

The answer to your problem is 15 if you need work here it is 

x=Quarters    y=Dimes

so the total number of coins is 35 the other equation is 
.25x+.1y= 6.5

Now we can solve for x and y easily 
y=35-x

We can substitute the into the other equation 
.25x+.1(35-x)=6.5

Lets Simplify it
.15x=3.5=6.5
.15x=3
x=20
Now we can sub stitute x=20 back into the first equation to get y and if we get x+y=35 then 20+y=35 we know that there are 15 dimes left over so 20+15=35

15 dimes
20 quarters=5$ +15 dimes = 1.50 which = 6.50 and 35 coins