Ajar of dimes and quarters contains 48 coins worth $7.50. what is the number of quarters and dimes?

So 48 coins, if they were all dimes, they'd be worth 48 * 10 cents or $4.80. But they're worth $7.50, which is $2.70 more. 

Now each coin that is a quarter adds 15 cents to the total, because a quarter is worth 15 cents more than a dime. Divide $2.70 by 15 cents and you get 18. That means that 18 of the 48 coins are quarters. 48-18 = 30, so there are 30 dimes. 

To check your answer, you can do the problem backwards. 30 dimes is $3. 18 quarters is $4.50. Add those two amounts together, and you get $7.50.