SOLUTION: Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. the number of quarters is 5 less then three-fourths of the number of dimes. the number of the

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. the number of quarters is 5 less then three-fourths of the number of dimes. the number of the       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 215332: Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. the number of quarters is 5 less then three-fourths of the number of dimes. the number of the silver dollares is 7 more then five-eighths of the number of dimes. how many coins of each kind are in her collection?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. the number of quarters is 5 less than three-fourths of the number of dimes. The number of the silver dollars is 7 more than five-eighths of the number of dimes. How many coins of each kind are in her collection?

Step 1. Let x be the number of dimes.

Step 2. Let 3x%2F4-5 be the number of quarters since number of quarters is 5 less then three-fourths of the number of dimes

Step 3. Let 5x%2F8%2B7 be the number of silver dollars since number of the silver dollars is 7 more than five-eighths of the number of dimes

Step 4. Then, x%2B3x%2F4-5%2B5x%2F8%2B7=116 since Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars.

Step 5. Simplify the equation in Step 4.

x%2B3x%2F4-5%2B5x%2F8%2B7=116

Multiply 24 to both sides of the equation to get rid of denominators.

24%2A%28x%2B3x%2F4-5%2B5x%2F8%2B7%29=24%2A116

24x%2B18x-120%2B15x%2B168=2784

57x%2B48=2784

57x=2784-48=2736

57x%2F57=2736%2F57

x=48

With x=48, then 3x%2F4-5=3%2A48%2F4-5=31 and 5x%2F8%2B7=5%2A48%2F8%2B7=37

Check total number of coins: 48+31+37=116 which is a true statement.

Step 6. The number of dimes is 31, the number of quarter is 31 and the number of silver dollars is 37.

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