SOLUTION: Your cable company offers two cable plans. One plan costs a monthly fee of $45 and $2 per additional channel. The other plan costs a monthly fee of $30 and $3 per additional channe

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Question 1188684: Your cable company offers two cable plans. One plan costs a monthly fee of $45 and $2 per additional channel. The other plan costs a monthly fee of $30 and $3 per additional channel. For how many extra channels will the cost be the same amount? What is that cost?
Found 2 solutions by Shin123, MathTherapy:
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
Let x be the number of additional channels. The first plan costs 45+2x and the other plan costs 30+3x. Setting them equal, you get .
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: 45+2x=30+3x simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( 45+2x=30+3x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved 45 to the right of expression
It becomes .
Look at .
Moved 30 to the right of expression
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-3%2Ax+%29,highlight_green%28+-30+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Moved 15 to the right of expression
It becomes .
Look at .
Eliminated similar terms highlight_red%28+2%2Ax+%29,highlight_red%28+-3%2Ax+%29 replacing them with highlight_green%28+%282-3%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -1
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29
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%2B15=0+%29 equivalent to -x+15 =0
It becomes .
Result:
This is an equation! Solutions: x=15.

Universal Simplifier and Solver


Done!

Therefore, 15 additional channels are needed for both plans to cost the same.
Plugging this value in to either equation, you get that cost is $75.
Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

Your cable company offers two cable plans. One plan costs a monthly fee of $45 and $2 per additional channel. The other plan costs a monthly fee of $30 and $3 per additional channel. For how many extra channels will the cost be the same amount? What is that cost?
Let number of additional channels be C
Then for plans to cost the same, we get: 2C + 45 = 3C + 30
2C - 3C = 30 - 45
    - C = - 15
Number of additional channels to make both plans cost the same, or 
Substitute value of C into either side of the equation to get the cost!

That's IT!! Could this be any simpler?
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