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

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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) About Me  (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 0.20x%2B0.25%2A%2832-x%29=7.40 was fully solved.
  • Text form: 0.20x+0.25*(32-x)=7.40 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+0.20x%2B0.25%2A%2832-x%29=7.40+%29
    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 0.20%2Ax%2B0.25%2A%28highlight_red%28+32+%29-x%29=7.40.
Moved 32 to the right of expression
It becomes 0.20%2Ax%2B0.25%2A%28-x%2Bhighlight_green%28+32+%29%29=7.40.
Look at 0.20%2Ax%2B0.25%2A%28-x%2B32%29=highlight_red%28+7.40+%29.
Moved these terms to the left highlight_green%28+-7.40+%29
It becomes 0.20%2Ax%2B0.25%2A%28-x%2B32%29-highlight_green%28+7.40+%29=0.
Look at 0.20%2Ax%2Bhighlight_red%28+0.25%2A%28-x%2B32%29+%29-7.40=0.
Expanded term 0.25 by using associative property on %28-x%2B32%29
It becomes 0.20%2Ax-highlight_green%28+0.25%2Ax+%29%2Bhighlight_green%28+0.25%2A32+%29-7.40=0.
Look at 0.20%2Ax-0.25%2Ax%2Bhighlight_red%28+0.25%2A32+%29-highlight_red%28+7.40+%29=0.
Replace constants in expression: highlight_red%28+0.25%2A32+%29,highlight_red%28+-7.40+%29 with highlight_green%28+0.6+%29
It becomes highlight_green%28+0.6+%29%2B0.20%2Ax-0.25%2Ax=0.
Look at highlight_red%28+0.6+%29%2B0.20%2Ax-0.25%2Ax=0.
Moved 0.6 to the right of expression
It becomes 0.20%2Ax-0.25%2Ax%2Bhighlight_green%28+0.6+%29=0.
Look at highlight_red%28+0.20%2Ax+%29-highlight_red%28+0.25%2Ax+%29%2B0.6=0.
Eliminated similar terms highlight_red%28+0.20%2Ax+%29,highlight_red%28+-0.25%2Ax+%29 replacing them with highlight_green%28+%280.20-0.25%29%2Ax+%29
It becomes highlight_green%28+%280.20-0.25%29%2Ax+%29%2B0.6=0.
Look at %28highlight_red%28+0.20+%29-highlight_red%28+0.25+%29%29%2Ax%2B0.6=0.
Added fractions or integers together
It becomes %28-highlight_green%28+5%2F100+%29%29%2Ax%2B0.6=0.
Look at highlight_red%28+%28-highlight_red%28+5%2F100+%29%29%2Ax+%29%2B0.6=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+1%2F100+%29
It becomes -highlight_green%28+5+%29%2Fhighlight_green%28+100+%29%2Ax%2B0.6=0.
Look at -highlight_red%28+5+%29%2Fhighlight_red%28+100+%29%2Ax%2B0.6=0.
Factors 5 and 100 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes -highlight_green%28+1+%29%2Fhighlight_green%28+20+%29%2Ax%2B0.6=0.
Look at -highlight_red%28+1+%29%2F20%2Ax%2B0.6=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2F20%2B0.6=0.
Look at highlight_red%28+-x%2F20%2B0.6+%29=0.
Solved linear equation highlight_red%28+-x%2F20%2B0.6=0+%29 equivalent to -0.05*x+0.6 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
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