# 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

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Coins -> 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      Log On

 Ad: Over 600 Algebra Word Problems at edhelper.com Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Word Problems: Coins Solvers Lessons Answers archive Quiz In Depth

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

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

 Here's what you tried: This is an equation! Solutions: x=7. Graphical form: Equation was fully solved.Text form: 0.05x+0.25*(16-x)=2.60 simplifies to 0=0Cartoon (animation) form: 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 .
Moved to the right of expression
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Replace constants in expression: , with
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor ,
It becomes .

Look at .
Factors 20 and 100 have greatest common factor (GCF) of 20. Reducing fraction.
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
Solved linear equation equivalent to -0.2*x+1.4 =0
It becomes .
Result:
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.