Ajar of dimes and quarters contains $15.25. there are 103 coins in all. how many of each are there.

Let x=number of quarters; value of quarters=0.25x
Then 103-x=number of dimes; value of dimes=0.10(103-x) 
Now we are told that the value of the quarters plus the value of the dimes equals $15.25. So our equation to solve is: 
0.25x+0.10(103-x)=$15.25 get rid of parens 
0.25x+10.30-0.10x=15.25 subtract 10.30 from both sides
0.25x+10.30-10.30-0.10x=15.25-10.30 collect like terms
0.15x=4.95 divide both sides by 0.15 

x=33number of quarters 
103-x=103-33=70number of dimes 
CK 
33*0.25+70*0.10=15.25
8.25+7.00=15.25
15.25=15.25 

Hope this helps