Question

Onefit, a new fitness center, starts with 100 members and grows by 20 members per month while the established fitness center bygym has 451 members (when onefit was built) and loses 19 members per month. (a) Write a linear equation to represent the number of members at onefit after months: (b) Write a linear equation to represent the number of members at bygym after months: (c) In how many months will the onefit have the same number of members as bygym? Round the time to the nearest whole number of months.

Answer 1

The linear equation to represent the number of members at Onefit after months is y = 100 + 20x. The linear equation to represent the number of members at Bygym after months is y = 451 - 19x. It will take approximately 9 months for Onefit to have the same number of members as Bygym.

Step-by-step explanation:

(a) Linear equation to represent the number of members at Onefit after months:

Let x be the number of months. Onefit starts with 100 members and grows by 20 members per month. So the linear equation representing the number of members at Onefit after months is:
y = 100 + 20x

(b) Linear equation to represent the number of members at Bygym after months:

Bygym starts with 451 members and loses 19 members per month. So the linear equation representing the number of members at Bygym after months is:
y = 451 - 19x

(c) In how many months will Onefit have the same number of members as Bygym?

To find the number of months when Onefit and Bygym have the same number of members, we need to solve the equation:
100 + 20x = 451 - 19x

Combining like terms:
39x = 351

Dividing both sides by 39:
x = 9

Therefore, it will take approximately 9 months for Onefit to have the same number of members as Bygym.