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

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) (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 was fully solved.
Text form: 0.05x+0.25*(16-x)=2.60 simplifies to 0=0
Cartoon (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 highlight_green%28+-2.60+%29

It becomes .

Look at .
Expanded term 0.25

by using associative property on %28-x%2B16%29

It becomes .

Look at .
Replace constants in expression: highlight_red%28+0.25%2A16+%29

with

It becomes .

Look at .
Moved 1.4

to the right of expression
It becomes .

Look at .
Eliminated similar terms highlight_red%28+0.05%2Ax+%29

replacing them with highlight_green%28+%280.05-0.25%29%2Ax+%29

It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+20+%29

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 highlight_red%28+1+%29

It becomes .

Look at .
Solved linear equation highlight_red%28+-x%2F5%2B1.4=0+%29

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.

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

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