SOLUTION: the difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. find both numbers

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Question 223553: the difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. find both numbers
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers

Step 1. Let x be one smaller number

Step 2. Let y be the larger number.

Step 3. Then -x+y=12 since the difference of two numbers is 12.

Step 4. 2y%2F5=6%2Bx%2F3 since two fifths of the greater number is six more than one third of the lesser number

Multiply by 15 to get rid of the denominators.

15%2A2y%2F5=15%2A6%2B15x%2F3

6y=90%2B5x

Subtract 5x from both sides of the equation

-5x%2B6y=90

Step 5. So here's our system of linear equations From Steps 3 and 4:

-x%2By=12
-5x%2B6y=90

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++-1%5Cx+%2B+1%5Cy+=+12%2C%0D%0A++++-5%5Cx+%2B+6%5Cy+=+90+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
-1%2Ax+=+12+-+1%2Ay, or x+=+12%2F-1+-+1%2Ay%2F-1. Substitute that
into another equation:
-5%2A%2812%2F-1+-+1%2Ay%2F-1%29+%2B+6%5Cy+=+90 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



Step 6. The numbers are 18 and 30.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J