SOLUTION: Joe Lick bought some 20-cent and 25-cent stamps. He bought 32 stamps in all, and paid $7.40 for them. How many stamps of each kind did he buy? Problem Solving:Using Charts

Question 226300: Joe Lick bought some 20-cent and 25-cent stamps. He bought 32 stamps in all, and paid $7.40 for them. How many stamps of each kind did he buy?
Problem Solving:Using Charts
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Joe Lick bought some 20-cent and 25-cent stamps. He bought 32 stamps in all, and paid $7.40 for them. How many stamps of each kind did he buy?

Step 1. Let x be the number of 20-cent stamps

Step 2. Let 32-x be the number of 25-cent stamps since there are 32 stamps in all.

Step 3. Let 0.20x be the dollar value of 20-cent stamps.

Step 4. Let 0.25(32-x) be the dollar value of 25-cent stamps.

Step 5. Then, 0.20x+0.25(32-x)=7.40 be the total dollar value of 7.40.

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=12.
Graphical form: Equation was fully solved.
Text form: 0.20x+0.25*(32-x)=7.40 simplifies to 0=0
Cartoon (animation) form:
For tutors: simplify_cartoon( 0.20x+0.25*(32-x)=7.40 )
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+-7.40+%29

It becomes .

Look at .
Expanded term 0.25

by using associative property on %28-x%2B32%29

It becomes .

Look at .
Replace constants in expression: highlight_red%28+0.25%2A32+%29

with

It becomes .

Look at .
Moved 0.6

to the right of expression
It becomes .

Look at .
Eliminated similar terms highlight_red%28+0.20%2Ax+%29

replacing them with highlight_green%28+%280.20-0.25%29%2Ax+%29

It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+5+%29

It becomes .

Look at .
Factors 5 and 100 have greatest common factor (GCF) of 5. 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%2F20%2B0.6=0+%29

equivalent to -0.05*x+0.6 =0
It becomes .
Result:
This is an equation! Solutions: x=12.

Universal Simplifier and Solver

Done!

With x=12 then 32-x=20

Check the total dollar value 0.20*12 + 0.25*20 =2.40+5.00=7.40 which is a true statement.

Step 7. ANSWER: The number of 20-cent stamps is 12 and the number of 25-cent stamps is 20.

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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