SOLUTION: Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamp

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Question 214746: Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy?
Found 2 solutions by drj, stanbon:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy?

Step 1. Let x be the number of 30 cents stamps.

Step 2. Let x-2 be the number of 20 cents stamps.

Step 3. Let 30x be the cost of buying x number of 30 cents stamps

Step 4. Let 20(x-2) be the cost of buying x-2 number of 20 cents stamps.

Step 5. 30x+20(x-2)=360 cents is the total cost of buying stamps.

Step 6. The following steps will solve the equation in Step 5:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=8.
  • Graphical form: Equation 30x%2B20%2A%28x-2%29=360 was fully solved.
  • Text form: 30x+20*(x-2)=360 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+30x%2B20%2A%28x-2%29=360+%29
    For tutors: simplify_cartoon( 30x+20*(x-2)=360 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 30%2Ax%2B20%2A%28x-2%29=highlight_red%28+360+%29.
Moved these terms to the left highlight_green%28+-360+%29
It becomes 30%2Ax%2B20%2A%28x-2%29-highlight_green%28+360+%29=0.
Look at 30%2Ax%2Bhighlight_red%28+20%2A%28x-2%29+%29-360=0.
Expanded term 20 by using associative property on %28x-2%29
It becomes 30%2Ax%2Bhighlight_green%28+20%2Ax+%29-highlight_green%28+20%2A2+%29-360=0.
Look at 30%2Ax%2B20%2Ax-highlight_red%28+20+%29%2Ahighlight_red%28+2+%29-360=0.
Multiplied numerator integers
It becomes 30%2Ax%2B20%2Ax-highlight_green%28+40+%29-360=0.
Look at 30%2Ax%2B20%2Ax-highlight_red%28+40+%29-highlight_red%28+360+%29=0.
Added fractions or integers together
It becomes 30%2Ax%2B20%2Ax%2Bhighlight_green%28+-400+%29=0.
Look at 30%2Ax%2B20%2Ax%2Bhighlight_red%28+-400+%29=0.
Removed extra sign in front of -400
It becomes 30%2Ax%2B20%2Ax-highlight_green%28+400+%29=0.
Look at highlight_red%28+30%2Ax+%29%2Bhighlight_red%28+20%2Ax+%29-400=0.
Eliminated similar terms highlight_red%28+30%2Ax+%29,highlight_red%28+20%2Ax+%29 replacing them with highlight_green%28+%2830%2B20%29%2Ax+%29
It becomes highlight_green%28+%2830%2B20%29%2Ax+%29-400=0.
Look at %28highlight_red%28+30+%29%2Bhighlight_red%28+20+%29%29%2Ax-400=0.
Added fractions or integers together
It becomes %28highlight_green%28+50+%29%29%2Ax-400=0.
Look at highlight_red%28+%28highlight_red%28+50+%29%29%2Ax+%29-400=0.
Remove unneeded parentheses around factor highlight_red%28+50+%29
It becomes highlight_green%28+50+%29%2Ax-400=0.
Look at highlight_red%28+50%2Ax-400+%29=0.
Solved linear equation highlight_red%28+50%2Ax-400=0+%29 equivalent to 50*x-400 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=8.

Universal Simplifier and Solver


Done!



With x=8, then x-2=6

Step 7 The number of 30 cents stamps is 8 and the number of 20 cents stamps is 6.

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

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy?
------------------------------------------------
Equations:
Quantity Eq.: w = r -2
Value Eq.::::20w + 30r = 360 cents
=========================================
Rearrange the Equations:
2w - 2r = -4
2w + 3r = 36
---------------------
Subtract the 1st from the 2nd:
5r = 40
r = 8 (# of thirty-cent stamps)
w = r-2, so w = 6 (# of twenty-cent stamps)
----------------
Checking
8*30+6*20 = 240 + 120 = 360 cents
====================================
Cheers,
Stan H.