SOLUTION: A coin operated washing machine contains $19.95 in nickels and quarters. If there is one less nickel than 3 times the number of quarters, how many of each are there?

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Question 221298: A coin operated washing machine contains $19.95 in nickels and quarters. If there is one less nickel than 3 times the number of quarters, how many of each are there?
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A coin operated washing machine contains $19.95 in nickels and quarters. If there is one less nickel than 3 times the number of quarters, how many of each are there?

Step 1. Let x be the number of nickels.

Step 2. Let 0.05x be the dollar value of nickels.

Step 3. Let y be the number of quarters.

Step 4. Let 0.25y be the dollar value of quarters.

Step 5. 0.05x+0.25y=19.95 or 5x+25y=1995since coin operated washing machine contains $19.95 in nickels and quarters.

Step 6. x+1=3y or x-3y=-1 since there is one less nickel than 3 times the number of quarters

Step 7. We have linear system of equations in Steps 5 and 6.

5x+25y=1995
x-3y=-1


Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++5%5Cx+%2B+25%5Cy+=+1995%2C%0D%0A++++1%5Cx+%2B+-3%5Cy+=+-1+%29%0D%0A++We'll use substitution. After moving 25*y to the right, we get:
5%2Ax+=+1995+-+25%2Ay, or x+=+1995%2F5+-+25%2Ay%2F5. Substitute that
into another equation:
1%2A%281995%2F5+-+25%2Ay%2F5%29+%2B+-3%5Cy+=+-1 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



x=149 and y=50

Check dollar value: 149*0.05+50*0.25=7.45+12.50=19.95 and there is one less nickel (149) than 3 times the number of quarters (3*50=150)...both are true statements.

Step 8. ANSWER: There are 149 nickels and 50 quarters.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by MathTherapy(639) About Me  (Show Source):
You can put this solution on YOUR website!
A coin operated washing machine contains $19.95 in nickels and quarters. If there is one less nickel than 3 times the number of quarters, how many of each are there?

Let the amount of quarters be Q

Since there is one less nickel than 3 times the number of quarters, then the amount of nickels = 3Q - 1

Now, since the value of the nickels and quarters is $19.95, we'll have:

.25(Q) + .05(3Q - 1) = 19.95

.25Q + .15Q - .05 = 19.95

.4Q - .05 = 19.95

.4Q = 19.95 + .05

.4Q = 20

The amount of quarters, or Q = 20%2F.4 = highlight_green%2850%29

The amount of nickels = highlight_green%28149%29 ---- (3 * 50 - 1 )