SOLUTION: John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find the number of dimes and quarters. –setup system of equations and give the solution

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Question 223618: John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution

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=2.05 be the total dollar value.

Step 6. Also, y=x+3 since there are 3 more dimes than quarters

Step 7. Our linear system of equation is given in Steps 4 and 5 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: So, we know that y=8. Since , x=5.

Answer: .



So x=5 and y=8. The difference is 3 and the total dollar value is 0.25*5+0.10*8=2.05 which is a true statement.

Step 8. ANSWER: The number of quarters is 5 and the number of dimes is 8.

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



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