SOLUTION: Company A’s revenue this fiscal year is $918,000 , but its revenue is decreasing by $18,000 each year. Company B’s revenue this fiscal year is $252,000 , and its revenue is in

Algebra ->  Expressions-with-variables -> SOLUTION: Company A’s revenue this fiscal year is $918,000 , but its revenue is decreasing by $18,000 each year. Company B’s revenue this fiscal year is $252,000 , and its revenue is in      Log On


   

Question 1188833: Company A’s revenue this fiscal year is $918,000 , but its revenue is decreasing by $18,000 each year. Company B’s revenue this fiscal year is $252,000 , and its revenue is increasing by $19,000 each year. Write and solve a system of equations to answer how many years after did Company B will catch up with Company A in revenue.
Found 2 solutions by Shin123, ikleyn:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of years after this fiscal year. Then, we have the equationcross%28s%29
918000-18000x=252000%2B19000x
Solving, we get
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=18.
  • Graphical form: Equation 918000-18000x=252000%2B19000x was fully solved.
  • Text form: 918000-18000x=252000+19000x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+918000-18000x=252000%2B19000x+%29
    For tutors: simplify_cartoon( 918000-18000x=252000+19000x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+918000+%29-18000%2Ax=252000%2B19000x.
Moved 918000 to the right of expression
It becomes -18000%2Ax%2Bhighlight_green%28+918000+%29=252000%2B19000x.
Look at -18000%2Ax%2B918000=highlight_red%28+252000+%29%2B19000%2Ax.
Moved 252000 to the right of expression
It becomes -18000%2Ax%2B918000=19000%2Ax%2Bhighlight_green%28+252000+%29.
Look at -18000%2Ax%2B918000=highlight_red%28+19000%2Ax%2B252000+%29.
Moved these terms to the left highlight_green%28+-19000%2Ax+%29,highlight_green%28+-252000+%29
It becomes -18000%2Ax%2B918000-highlight_green%28+19000%2Ax+%29-highlight_green%28+252000+%29=0.
Look at -18000%2Ax%2Bhighlight_red%28+918000+%29-19000%2Ax-highlight_red%28+252000+%29=0.
Added fractions or integers together
It becomes -18000%2Ax%2Bhighlight_green%28+666000+%29-19000%2Ax=0.
Look at -18000%2Ax%2Bhighlight_red%28+666000+%29-19000%2Ax=0.
Moved 666000 to the right of expression
It becomes -18000%2Ax-19000%2Ax%2Bhighlight_green%28+666000+%29=0.
Look at -highlight_red%28+18000%2Ax+%29-highlight_red%28+19000%2Ax+%29%2B666000=0.
Eliminated similar terms highlight_red%28+-18000%2Ax+%29,highlight_red%28+-19000%2Ax+%29 replacing them with highlight_green%28+%28-18000-19000%29%2Ax+%29
It becomes highlight_green%28+%28-18000-19000%29%2Ax+%29%2B666000=0.
Look at %28-highlight_red%28+18000+%29-highlight_red%28+19000+%29%29%2Ax%2B666000=0.
Added fractions or integers together
It becomes %28highlight_green%28+-37000+%29%29%2Ax%2B666000=0.
Look at %28highlight_red%28+-37000+%29%29%2Ax%2B666000=0.
Removed extra sign in front of -37000
It becomes %28-highlight_green%28+37000+%29%29%2Ax%2B666000=0.
Look at highlight_red%28+%28-highlight_red%28+37000+%29%29%2Ax+%29%2B666000=0.
Remove unneeded parentheses around factor highlight_red%28+37000+%29
It becomes -highlight_green%28+37000+%29%2Ax%2B666000=0.
Look at highlight_red%28+-37000%2Ax%2B666000+%29=0.
Solved linear equation highlight_red%28+-37000%2Ax%2B666000=0+%29 equivalent to -37000*x+666000 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=18.

Universal Simplifier and Solver


Done!

Therefore, it will take highlight%2818%29 years for company B's revenue to catch up to company A's.

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

            Do not consider the post from @Shin123 as an attempt to teach . . .

            These are his exercises playing with the solver,  for his self-satisfaction.


The true solution is in several lines. 

The equation is, OBVIOUSLY


    918000 - 18000x = 252000 + 19000x


Simplify and find x


    19000x + 18000x = 918000 - 252000

         37000x     =     666000

              x     =     666000/37000 = 18 years.

Solved.