Question

Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many quarters does he have?

Answer 1

You can represent this as a system of equations. Let's call dimes D and quarters Q. The number of dimes is three more than three times the number of quarters, so D=3Q+3. Also, .1D+.25Q=6.35 because a dime is worth 1/10 of a dollar and a quarter is worth 1/4 of a dollar. Now, you can use the substitution method to combine the equations. Lets put them in terms of D. The first one is already done. For the second one, subtract the second term over to get .1D=6.35-.25Q. Then, divide off the .1. This gives you D=63.5-2.5Q. Now, set them equal to each other. 3Q+3=63.5-2.5Q. Solve it to get 6.5Q=60.5. That gives you Q=9.31. Since you can't have .31 quarters, the answer is 9.