SOLUTION: You have 15 coins in your pocket that are either quarters or nickles. the total $2.75. how many of each coin do you have?

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: You have 15 coins in your pocket that are either quarters or nickles. the total $2.75. how many of each coin do you have?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 215018: You have 15 coins in your pocket that are either quarters or nickles. the total $2.75. how many of each coin do you have?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
You have 15 coins in your pocket that are either quarters or nickles. the total $2.75. how many of each coin do you have?

Step 1. Let x be the number of quarters and 15-x be the number of nickles.

Step 2. Let 0.25x be the cost for x number of quarters.

Step 3. Let 0.05(15-x) be the cost for 15-x number of nickles.

Step 4. 0.25x+0.05(15-x)=2.75 where we added Steps 1 and 2.

Step 5. The following will solve the equation in Step 4.

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


YOUR ANSWER


  • This is an equation! Solutions: x=10.
  • Graphical form: Equation 0.25x%2B0.05%2A%2815-x%29=2.75 was fully solved.
  • Text form: 0.25x+0.05*(15-x)=2.75 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+0.25x%2B0.05%2A%2815-x%29=2.75+%29
    For tutors: simplify_cartoon( 0.25x+0.05*(15-x)=2.75 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 0.25%2Ax%2B0.05%2A%28highlight_red%28+15+%29-x%29=2.75.
Moved 15 to the right of expression
It becomes 0.25%2Ax%2B0.05%2A%28-x%2Bhighlight_green%28+15+%29%29=2.75.
Look at 0.25%2Ax%2B0.05%2A%28-x%2B15%29=highlight_red%28+2.75+%29.
Moved these terms to the left highlight_green%28+-2.75+%29
It becomes 0.25%2Ax%2B0.05%2A%28-x%2B15%29-highlight_green%28+2.75+%29=0.
Look at 0.25%2Ax%2Bhighlight_red%28+0.05%2A%28-x%2B15%29+%29-2.75=0.
Expanded term 0.05 by using associative property on %28-x%2B15%29
It becomes 0.25%2Ax-highlight_green%28+0.05%2Ax+%29%2Bhighlight_green%28+0.05%2A15+%29-2.75=0.
Look at 0.25%2Ax-0.05%2Ax%2Bhighlight_red%28+0.05%2A15+%29-highlight_red%28+2.75+%29=0.
Replace constants in expression: highlight_red%28+0.05%2A15+%29,highlight_red%28+-2.75+%29 with highlight_green%28+-2+%29
It becomes highlight_green%28+-2+%29%2B0.25%2Ax-0.05%2Ax=0.
Look at highlight_red%28+-2+%29%2B0.25%2Ax-0.05%2Ax=0.
Moved -2 to the right of expression
It becomes 0.25%2Ax-0.05%2Ax%2Bhighlight_green%28+-2+%29=0.
Look at 0.25%2Ax-0.05%2Ax%2Bhighlight_red%28+-2+%29=0.
Removed extra sign in front of -2
It becomes 0.25%2Ax-0.05%2Ax-highlight_green%28+2+%29=0.
Look at highlight_red%28+0.25%2Ax+%29-highlight_red%28+0.05%2Ax+%29-2=0.
Eliminated similar terms highlight_red%28+0.25%2Ax+%29,highlight_red%28+-0.05%2Ax+%29 replacing them with highlight_green%28+%280.25-0.05%29%2Ax+%29
It becomes highlight_green%28+%280.25-0.05%29%2Ax+%29-2=0.
Look at %28highlight_red%28+0.25+%29-highlight_red%28+0.05+%29%29%2Ax-2=0.
Added fractions or integers together
It becomes %28highlight_green%28+20%2F100+%29%29%2Ax-2=0.
Look at highlight_red%28+%28highlight_red%28+20%2F100+%29%29%2Ax+%29-2=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-2=0.
Look at highlight_red%28+20+%29%2Fhighlight_red%28+100+%29%2Ax-2=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-2=0.
Look at highlight_red%28+1+%29%2F5%2Ax-2=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F5-2=0.
Look at highlight_red%28+x%2F5-2+%29=0.
Solved linear equation highlight_red%28+x%2F5-2=0+%29 equivalent to 0.2*x-2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=10.

Universal Simplifier and Solver


Done!



With x=10, then 10-x=5. Let's check total value 0.25*10+0.05*5=2.50+0.25=2.70 ...so it checks out.

Step 6. ANSWER. The number of quarters is 10 and the number of nickels is 5.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J