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?

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) (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 was fully solved.
Text form: 0.25x+0.05*(15-x)=2.75 simplifies to 0=0
Cartoon (animation) form:
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 .
Moved

to the right of expression
It becomes .

Look at .
Moved these terms to the left highlight_green%28+-2.75+%29

It becomes .

Look at .
Expanded term 0.05

by using associative property on %28-x%2B15%29

It becomes .

Look at .
Replace constants in expression: highlight_red%28+0.05%2A15+%29

with

It becomes .

Look at .
Moved

to the right of expression
It becomes .

Look at .
Removed extra sign in front of

It becomes .

Look at .
Eliminated similar terms highlight_red%28+0.25%2Ax+%29

replacing them with highlight_green%28+%280.25-0.05%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%2F5-2=0+%29

equivalent to 0.2*x-2 =0
It becomes .
Result:
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

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