SOLUTION: Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have?

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Question 227657: Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have?

Step 1. Let x be the number of dimes

Step 2. Let 24-x be the number of quarters since there are 16 coins in all.

Step 3. Let 0.10x be the dollar value of dimes.

Step 4. Let 0.25(24-x) be the dollar value of quarters.

Step 5. Then, 0.10x+0.25(24-x)=3.75 be the total dollar value of 3.75.

Step 6. Solving the equation in Step 5 yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=15.
  • Graphical form: Equation 0.10x%2B0.25%2A%2824-x%29=3.75 was fully solved.
  • Text form: 0.10x+0.25*(24-x)=3.75 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+0.10x%2B0.25%2A%2824-x%29=3.75+%29
    For tutors: simplify_cartoon( 0.10x+0.25*(24-x)=3.75 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 0.10%2Ax%2B0.25%2A%28highlight_red%28+24+%29-x%29=3.75.
Moved 24 to the right of expression
It becomes 0.10%2Ax%2B0.25%2A%28-x%2Bhighlight_green%28+24+%29%29=3.75.
Look at 0.10%2Ax%2B0.25%2A%28-x%2B24%29=highlight_red%28+3.75+%29.
Moved these terms to the left highlight_green%28+-3.75+%29
It becomes 0.10%2Ax%2B0.25%2A%28-x%2B24%29-highlight_green%28+3.75+%29=0.
Look at 0.10%2Ax%2Bhighlight_red%28+0.25%2A%28-x%2B24%29+%29-3.75=0.
Expanded term 0.25 by using associative property on %28-x%2B24%29
It becomes 0.10%2Ax-highlight_green%28+0.25%2Ax+%29%2Bhighlight_green%28+0.25%2A24+%29-3.75=0.
Look at 0.10%2Ax-0.25%2Ax%2Bhighlight_red%28+0.25%2A24+%29-highlight_red%28+3.75+%29=0.
Replace constants in expression: highlight_red%28+0.25%2A24+%29,highlight_red%28+-3.75+%29 with highlight_green%28+2.25+%29
It becomes highlight_green%28+2.25+%29%2B0.10%2Ax-0.25%2Ax=0.
Look at highlight_red%28+2.25+%29%2B0.10%2Ax-0.25%2Ax=0.
Moved 2.25 to the right of expression
It becomes 0.10%2Ax-0.25%2Ax%2Bhighlight_green%28+2.25+%29=0.
Look at highlight_red%28+0.10%2Ax+%29-highlight_red%28+0.25%2Ax+%29%2B2.25=0.
Eliminated similar terms highlight_red%28+0.10%2Ax+%29,highlight_red%28+-0.25%2Ax+%29 replacing them with highlight_green%28+%280.10-0.25%29%2Ax+%29
It becomes highlight_green%28+%280.10-0.25%29%2Ax+%29%2B2.25=0.
Look at %28highlight_red%28+0.10+%29-highlight_red%28+0.25+%29%29%2Ax%2B2.25=0.
Added fractions or integers together
It becomes %28-highlight_green%28+15%2F100+%29%29%2Ax%2B2.25=0.
Look at highlight_red%28+%28-highlight_red%28+15%2F100+%29%29%2Ax+%29%2B2.25=0.
Remove unneeded parentheses around factor highlight_red%28+15+%29,highlight_red%28+1%2F100+%29
It becomes -highlight_green%28+15+%29%2Fhighlight_green%28+100+%29%2Ax%2B2.25=0.
Look at -highlight_red%28+15+%29%2Fhighlight_red%28+100+%29%2Ax%2B2.25=0.
Factors 15 and 100 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes -highlight_green%28+3+%29%2Fhighlight_green%28+20+%29%2Ax%2B2.25=0.
Look at highlight_red%28+-3%2F20%2Ax%2B2.25+%29=0.
Solved linear equation highlight_red%28+-3%2F20%2Ax%2B2.25=0+%29 equivalent to -0.15*x+2.25 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=15.

Universal Simplifier and Solver


Done!



With x=15 then 24-x=9

Check the total dollar value 0.10*15 + 0.25*9 =1.50+2.25=3.75 which is a true statement.

Step 7. ANSWER: The number of dimes is 15 and the number of quarters is 9.

I hope the above steps and explanation 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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV