# SOLUTION: A mixture of dimes and quarters has a total value of \$10.20. There are 57 coins in all. How many of each type are present?

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Question 223797: A mixture of dimes and quarters has a total value of \$10.20. There are 57 coins in all. How many of each type are present?
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A mixture of dimes and quarters has a total value of \$10.20. There are 57 coins in all. How many of each type are present?

Step 1. Let x be the number of quarters.

Step 2. Let 0.25x be the dollar value of quarters.

Step 3. Let y be the number of dimes.

Step 4. Let 0.10y be the dollar value of dimes.

Step 5. Then 0.25x+0.10y=10.20 be the total dollar value.

Step 6. Also, x+y=57 since there are 57 coins

Step 7. Our linear system of equation is given in Steps 4 and 5 is shown below:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 0.1*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101

So x=30 and y=27. The difference is 3 and the total dollar value is 0.25*30+0.10*27=7.50+2.70=10.20 which is a true statement. And the total number of coins is 57.

Step 8. ANSWER: The number of quarters is 30 and the number of dimes is 27.

I hope the above steps were helpful.

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