Math Help please

Question

Russell wants to join fitness centre. Absmazing gym costs $200 to join and then $50 per month. Chubby Fitness Center cost $350 to join and then $40 per month. When will both cost the same amount and what will the cost be?

Answer 1

Russell wants to join fitness centre. Absmazing gym costs $200 to join and then $50 per month. Chubby Fitness Center cost $350 to join and then $40 per month. When will both cost the same amount and what will the cost be?

Let m = monthly price

Set up equations

Cost of Absmazing = 200 + 50m

Cost of Chubby = 350 +40m

Question is when will cost of abmazing equal cost of chubby, aka:

when will 200+50m equal 350+40m

... 200 + 50m = 350 + 40m

and solve for m

200 + 50m = 350 + 40m

50m + 200 = 40m + 350

50m +200 - 350 = 40m +350 - 350

50m - 150 = 40m

-50m + 50m - 150 = -50m + 40m

-150 = -10m

multiple each side by -1

150 = 10m

divide each side by 10

150/10 = m

simplify

15 = m

So in 15 months, the costs will equalize for the gyms

... to find how much you've paid in 15 months, plug in for m in the original equations

200 + 50(15) = 200 + 750 = 950$

double check your work with the second equation:

350 + 40(15) = 350 + 600 = 950$

Answer: $950 in 15 months