SOLUTION: Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have?

Question 227657: Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Jerry has 24 coins, all of which are either quarters and dimes. Their combined total equals $3.75. How many coins of each does Jerry have?

Step 1. Let x be the number of dimes

Step 2. Let 24-x be the number of quarters since there are 16 coins in all.

Step 3. Let 0.10x be the dollar value of dimes.

Step 4. Let 0.25(24-x) be the dollar value of quarters.

Step 5. Then, 0.10x+0.25(24-x)=3.75 be the total dollar value of 3.75.

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=15.
Graphical form: Equation was fully solved.
Text form: 0.10x+0.25*(24-x)=3.75 simplifies to 0=0
Cartoon (animation) form:
For tutors: simplify_cartoon( 0.10x+0.25*(24-x)=3.75 )
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+-3.75+%29

It becomes .

Look at .
Expanded term 0.25

by using associative property on %28-x%2B24%29

It becomes .

Look at .
Replace constants in expression: highlight_red%28+0.25%2A24+%29

with

It becomes .

Look at .
Moved 2.25

to the right of expression
It becomes .

Look at .
Eliminated similar terms highlight_red%28+0.10%2Ax+%29

replacing them with highlight_green%28+%280.10-0.25%29%2Ax+%29

It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+15+%29

It becomes .

Look at .
Factors 15 and 100 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes .

Look at .
Solved linear equation highlight_red%28+-3%2F20%2Ax%2B2.25=0+%29

equivalent to -0.15*x+2.25 =0
It becomes .
Result:
This is an equation! Solutions: x=15.

Universal Simplifier and Solver

Done!

With x=15 then 24-x=9

Check the total dollar value 0.10*15 + 0.25*9 =1.50+2.25=3.75 which is a true statement.

Step 7. ANSWER: The number of dimes is 15 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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