SOLUTION: I have a jar containing 80 coins either nickels or quarters total value is $14.60 How many of each coin do I have

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I have a jar containing 80 coins either nickels or quarters total value is $14.60 How many of each coin do I have      Log On


   

Question 220971: I have a jar containing 80 coins
either nickels or quarters
total value is $14.60
How many of each coin do I have
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
I have a jar containing 80 coins
either nickels or quarters
total value is $14.60
How many of each coin do I have

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=14.60 as given by the problem.

Step 6. x+y=80

Step 7. Then we have a system of equation in Steps 5 and 6.

0.05x+0.25y=14.60
x+y=80

OR

5x+25y=1460
x+y=80

Step 8. Solving using the substitution method yields.


Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++5%5Cx+%2B+25%5Cy+=+1460%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+80+%29%0D%0A++We'll use substitution. After moving 25*y to the right, we get:
5%2Ax+=+1460+-+25%2Ay, or x+=+1460%2F5+-+25%2Ay%2F5. Substitute that
into another equation:
1%2A%281460%2F5+-+25%2Ay%2F5%29+%2B+1%5Cy+=+80 and simplify: So, we know that y=53. Since x+=+1460%2F5+-+25%2Ay%2F5, x=27.

Answer: system%28+x=27%2C+y=53+%29.




Check 27*0.05+53*0.25=14.60...which is a true statement.

Step 9. Then number of nickels is 27 and the number of quarters is 53.

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