Big Gym Fitness charges $22 per month for a membership. All-Day Fitness charges $20 per month plus $50 membership fee. After how many months will the total amount paid to the two fitness clubs be the same?

25 months

Step-by-step explanation:

Big Gym Fitness charges $22 per month for a membership.

After x months, the charges will be:

22 * x = 22x

All-Day Fitness charges $20 per month plus $50 membership fee.

The membership fee is a one time payment. Hence, after x months, the charges will be:

50 + 20*x = 50 + 20x

After a certain number of months (x months) , the two fitness clubs will have the same charges. This occurs when:

22x = 50 + 20x

Hence, solving for x:

22x - 20x = 50

2x = 50

x = 50 / 2 = 25 months.

Their charges will be the same after 25 months.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

f is the midpoint of