SOLUTION: A collection of nickels and quarters amounts to $2.60. There are 16 coins in all. How many of each coin are there? Problem Solving:Using Charts

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Question 226298: A collection of nickels and quarters amounts to $2.60. There are 16 coins in all. How many of each coin are there?
Problem Solving:Using Charts
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A collection of nickels and quarters amounts to $2.60. There are 16 coins in all. How many of each coin are there?

Step 1. Let x be the number of nickels

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

Step 3. Let 0.05x be the dollar value of nickels.

Step 4. Let 0.25(16-x) be the dollar value of quarters.

Step 5. Then, 0.05x+0.25(16-x)=2.60 be the total dollar value of 2.60.

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=7.
  • Graphical form: Equation 0.05x%2B0.25%2A%2816-x%29=2.60 was fully solved.
  • Text form: 0.05x+0.25*(16-x)=2.60 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+0.05x%2B0.25%2A%2816-x%29=2.60+%29
    For tutors: simplify_cartoon( 0.05x+0.25*(16-x)=2.60 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 0.05%2Ax%2B0.25%2A%28highlight_red%28+16+%29-x%29=2.60.
Moved 16 to the right of expression
It becomes 0.05%2Ax%2B0.25%2A%28-x%2Bhighlight_green%28+16+%29%29=2.60.
Look at 0.05%2Ax%2B0.25%2A%28-x%2B16%29=highlight_red%28+2.60+%29.
Moved these terms to the left highlight_green%28+-2.60+%29
It becomes 0.05%2Ax%2B0.25%2A%28-x%2B16%29-highlight_green%28+2.60+%29=0.
Look at 0.05%2Ax%2Bhighlight_red%28+0.25%2A%28-x%2B16%29+%29-2.60=0.
Expanded term 0.25 by using associative property on %28-x%2B16%29
It becomes 0.05%2Ax-highlight_green%28+0.25%2Ax+%29%2Bhighlight_green%28+0.25%2A16+%29-2.60=0.
Look at 0.05%2Ax-0.25%2Ax%2Bhighlight_red%28+0.25%2A16+%29-highlight_red%28+2.60+%29=0.
Replace constants in expression: highlight_red%28+0.25%2A16+%29,highlight_red%28+-2.60+%29 with highlight_green%28+1.4+%29
It becomes highlight_green%28+1.4+%29%2B0.05%2Ax-0.25%2Ax=0.
Look at highlight_red%28+1.4+%29%2B0.05%2Ax-0.25%2Ax=0.
Moved 1.4 to the right of expression
It becomes 0.05%2Ax-0.25%2Ax%2Bhighlight_green%28+1.4+%29=0.
Look at highlight_red%28+0.05%2Ax+%29-highlight_red%28+0.25%2Ax+%29%2B1.4=0.
Eliminated similar terms highlight_red%28+0.05%2Ax+%29,highlight_red%28+-0.25%2Ax+%29 replacing them with highlight_green%28+%280.05-0.25%29%2Ax+%29
It becomes highlight_green%28+%280.05-0.25%29%2Ax+%29%2B1.4=0.
Look at %28highlight_red%28+0.05+%29-highlight_red%28+0.25+%29%29%2Ax%2B1.4=0.
Added fractions or integers together
It becomes %28-highlight_green%28+20%2F100+%29%29%2Ax%2B1.4=0.
Look at highlight_red%28+%28-highlight_red%28+20%2F100+%29%29%2Ax+%29%2B1.4=0.
Remove unneeded parentheses around factor highlight_red%28+20+%29,highlight_red%28+1%2F100+%29
It becomes -highlight_green%28+20+%29%2Fhighlight_green%28+100+%29%2Ax%2B1.4=0.
Look at -highlight_red%28+20+%29%2Fhighlight_red%28+100+%29%2Ax%2B1.4=0.
Factors 20 and 100 have greatest common factor (GCF) of 20. Reducing fraction.
It becomes -highlight_green%28+1+%29%2Fhighlight_green%28+5+%29%2Ax%2B1.4=0.
Look at -highlight_red%28+1+%29%2F5%2Ax%2B1.4=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2F5%2B1.4=0.
Look at highlight_red%28+-x%2F5%2B1.4+%29=0.
Solved linear equation highlight_red%28+-x%2F5%2B1.4=0+%29 equivalent to -0.2*x+1.4 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=7.

Universal Simplifier and Solver


Done!



With x=7 then 16-x=9

Check the total dollar value 0.05*7 + 0.25*9 =0.35+2.25=2.60 which is a true statement.

Step 7. ANSWER: The number of nickels is 7 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