Question

11. HEALTH CLUB Currently, 96 members participate in the morning workout,

and this number has been increasing by 2 people per week. Currently, 80
members participate in the afternoon workout, and this number has been
decreasing by 3 people per week. In how many weeks will the number of
people working out in the morning be double the number of people
working out in the afternoon?

Answer 1

mx + b = y

2x + 96 = y

-3x + 80 = z

What we want is y to be twice z, or y = 2z

If we're going to make 2z, then that means its equation needs to be doubled as well:

2x + 96 = 2(-3x + 80)

2x + 96 = -6x + 160

8x = 64

x = 8

Now to check our answer:

2 * 8 + 96

16 + 96 = 112

-3 * 8 + 80

-24 + 80 = 56

56 * 2 = 112

So morning membership will be double in 8 weeks.