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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (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 45%2B2x=30%2B3x.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=15.
  • Graphical form: Equation 45%2B2x=30%2B3x was fully solved.
  • Text form: 45+2x=30+3x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+45%2B2x=30%2B3x+%29
    For tutors: simplify_cartoon( 45+2x=30+3x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+45+%29%2B2%2Ax=30%2B3x.
Moved 45 to the right of expression
It becomes 2%2Ax%2Bhighlight_green%28+45+%29=30%2B3x.
Look at 2%2Ax%2B45=highlight_red%28+30+%29%2B3%2Ax.
Moved 30 to the right of expression
It becomes 2%2Ax%2B45=3%2Ax%2Bhighlight_green%28+30+%29.
Look at 2%2Ax%2B45=highlight_red%28+3%2Ax%2B30+%29.
Moved these terms to the left highlight_green%28+-3%2Ax+%29,highlight_green%28+-30+%29
It becomes 2%2Ax%2B45-highlight_green%28+3%2Ax+%29-highlight_green%28+30+%29=0.
Look at 2%2Ax%2Bhighlight_red%28+45+%29-3%2Ax-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes 2%2Ax%2Bhighlight_green%28+15+%29-3%2Ax=0.
Look at 2%2Ax%2Bhighlight_red%28+15+%29-3%2Ax=0.
Moved 15 to the right of expression
It becomes 2%2Ax-3%2Ax%2Bhighlight_green%28+15+%29=0.
Look at highlight_red%28+2%2Ax+%29-highlight_red%28+3%2Ax+%29%2B15=0.
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 highlight_green%28+%282-3%29%2Ax+%29%2B15=0.
Look at %28highlight_red%28+2+%29-highlight_red%28+3+%29%29%2Ax%2B15=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2Ax%2B15=0.
Look at %28highlight_red%28+-1+%29%29%2Ax%2B15=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2Ax%2B15=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2Ax+%29%2B15=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2Ax%2B15=0.
Look at -highlight_red%28+1+%29%2Ax%2B15=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2B15=0.
Look at highlight_red%28+-x%2B15+%29=0.
Solved linear equation highlight_red%28+-x%2B15=0+%29 equivalent to -x+15 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
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) About Me  (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?