Question

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

x = the amount of weeks
The equation: 96 +2x=2(80-3x)
=> x = 8

Answer 2

We have two linear equations, and we want to see when the value of one is twice the value of the other.

The answer is 8 weeks.

First, let's find the two equations.

Currently, in the morning workout, there are 96 members and the number has been increasing by 2 per week.

Then the number of morning members is given by:

M(w) = 96 + 2*w

where w represents the number of weeks.

For the afternoon, currently, there are 80 members, and this number decreases by 3 per week, then we have:

A(w) = 80 - 3*w

We want to see for which value of w we have that:

M(w) = 2*A(w)

So we must solve:

(96 + 2*w) = 2*(80 - 3*w)

96 + 2*w = 160 - 6*w

2*w + 6*w = 160 - 96

8*w = 64

w = 64/8 = 8

This means that after 8 weeks the number of people working out in the morning will be double the number of people working out in the afternoon.

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