SOLUTION: laura has $4.50 in quarters and dimes. She has 3 more dimes than quarters.How many quarters does she have?

Question 269192: laura has $4.50 in quarters and dimes. She has 3 more dimes than quarters.How many quarters does she have?
Answer by suhasbhat(3) (Show Source): You can put this solution on YOUR website!
Let Q be the number of quarters and D be the number of dimes.
The value of a quarter is 25 cents and the value of a dime is 10 cents.
The value of all the quarters together is 25 times the total number of quarters, so 25Q. The value of all the dimes together, following the same pattern, is 10D.
The total value together is $4.50, or 450 cents.
Therefore, 25Q+10D=450. But because she has 3 dimes more than quarters, Q+3=D.
By substitution 25Q+10(Q+3)=450
25Q+10Q+30=450
35Q=420
Q=420/35
Q=12.
There are 12 quarters.
Check:
If there are 12 quarters, then there are 3 more dimes.Thus, there are 15 dimes.
Now, if you substitute the numbers back into the equation you get:
25(12)+10(15)=450 (?)
300+150=450 true
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