Stu wants to join a gym. Fit-Place charges a $150 startup fee and then $25 per month. The Factory has no startup fee but charges $50 per month. Create a table showing the total cost for the first 8 months. Determine the month at which the total cost is the same.

Fit-Place charges a $135 startup fee and then $35 per month.

Means the cost here will be based on the equation :  where x is the number of months.

The Factory has no startup fee but charges $60 per month. Here the equation will be , where x is the number of months.

Step-by-step explanation:

Months              1          2          3        4         5        6          7        8

Fit-Place          170      205     240     275     310     345    380   415

The Factory     60      120        180     240    300    360   420    480

The total cost will be same in:

=>

=>

x = 5.4 rounded to 5 months.

Now we can see that the total cost will be same in almost 5 months.

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus