Zoe is comparing two local yoga programs. yo-yoga charges a $35 registration fee and $90 a month. essence yoga charges a registration fee of $75 and $80 per month. after how many months will the 2 programs be the same?

After 4 months

Step-by-step explanation:

The cost at both the programs consists of a "fixed cost" (reg fee)  & "variable cost" ( per month fee).

Let number of months be "x"

Yo-Yoga:

35 fixed

90 per month

So equation would be: 35 + 90x

Essence Yoga:

75 fixed

80 per month

So equation would be: 75 + 80x

To find number of month when cost would be same, we equate both equations and solve for x:

35 + 90x = 75 + 80x

10x = 40

x = 40/10

x = 4

hence, after 4 months, both cost would be same