SOLUTION: Bonnie has twice as many dimes as quarters, and nine more nickels than quarters. The value of his coins is $2.45. How many of each kind of coin does he have?

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Bonnie has twice as many dimes as quarters, and nine more nickels than quarters. The value of his coins is $2.45. How many of each kind of coin does he have?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 215524: Bonnie has twice as many dimes as quarters, and nine more nickels than quarters. The value of his coins is $2.45. How many of each kind of coin does he have?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Bonnie has twice as many dimes as quarters, and nine more nickels than quarters. The value of his coins is $2.45. How many of each kind of coin does he have?

Step 1. Let x be the number of quarters and 0.25x dollar value of x quarters.

Step 2. Let 2x be the number of dimes and 0.10*2x=.20x dollar value of 2x dimes.

Step 3. Let x+9 be the number of nickels and .05(x+9)=0.05x+0.45 dollar value of x+9 nickels.

Step 4. Then, total value is 0.25x+0.20x+0.05x+0.45=2.45. Solving yields the following steps.

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


YOUR ANSWER


  • This is an equation! Solutions: x=4.
  • Graphical form: Equation 0.25x%2B0.20x%2B0.05x%2B0.45=2.45 was fully solved.
  • Text form: 0.25x+0.20x+0.05x+0.45=2.45 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+0.25x%2B0.20x%2B0.05x%2B0.45=2.45+%29
    For tutors: simplify_cartoon( 0.25x+0.20x+0.05x+0.45=2.45 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+0.25%2Ax+%29,highlight_red%28+0.20%2Ax+%29,highlight_red%28+0.05%2Ax+%29 replacing them with highlight_green%28+%280.25%2B0.20%2B0.05%29%2Ax+%29
It becomes highlight_green%28+%280.25%2B0.20%2B0.05%29%2Ax+%29%2B0.45=2.45.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+50%2F100+%29%29%2Ax%2B0.45=2.45.
Look at highlight_red%28+%28highlight_red%28+50%2F100+%29%29%2Ax+%29%2B0.45=2.45.
Remove unneeded parentheses around factor highlight_red%28+50+%29,highlight_red%28+1%2F100+%29
It becomes highlight_green%28+50+%29%2Fhighlight_green%28+100+%29%2Ax%2B0.45=2.45.
Look at highlight_red%28+50+%29%2Fhighlight_red%28+100+%29%2Ax%2B0.45=2.45.
Factors 50 and 100 have greatest common factor (GCF) of 50. Reducing fraction.
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2Ax%2B0.45=2.45.
Look at highlight_red%28+1+%29%2F2%2Ax%2B0.45=2.45.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F2%2B0.45=2.45.
Look at x%2F2%2B0.45=highlight_red%28+2.45+%29.
Moved these terms to the left highlight_green%28+-2.45+%29
It becomes x%2F2%2B0.45-highlight_green%28+2.45+%29=0.
Look at x%2F2%2Bhighlight_red%28+0.45+%29-highlight_red%28+2.45+%29=0.
Added fractions or integers together
It becomes x%2F2-highlight_green%28+200%2F100+%29=0.
Look at highlight_red%28+x%2F2-200%2F100+%29=0.
Solved linear equation highlight_red%28+x%2F2-200%2F100=0+%29 equivalent to 0.5*x-2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=4.

Universal Simplifier and Solver


Done!



With x=4 , then 2x=8 and x+9=13

Check total...4*0.25+8*0.10+13*.05=1.00+0.80+0.65=2.45 which is a true statement.

Step 5. The number of quarters is 4 , the number of dimes is 8 , and the number of nickels is 13 .

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