SOLUTION: Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica has. If they both have the same amount of money, what coins do each have?

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Let's denote the number of dimes Jessica has by d and the number of quarters she has by q.
The first sentence tells us that:

Whitney has twice as many dimes (2d) and 1/3 as many quarters (1/3q) and they have the same amount of money. We could try to say , but that's not true, as d and q have different value. Our equation, with the weight of the values in, is:

We can simplify it by multiplying the 2, getting:

Then, we can subtract 20d and from both sides of the equation and solve the system:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve: We'll use substitution. After moving 1*q 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 Therefore, Jessica has 10 dimes and 6 quarters, and Whitney has 2*10 = 20 dimes and 1/3 * 6 = 2 quarters. We can check by seeing that 10*10 + 25*6 = 250, and 20*10 + 25*2 is also 250.