A fitness center offers two membership plans. Plan A requires a one-time enrollment fee of… — Armed Services Vocational Aptitude Battery (ASVAB)

A fitness center offers two membership plans. Plan A requires a one-time enrollment fee of $45$ dollars and costs $30$ dollars per month. Plan B requires a one-time enrollment fee of $105$ dollars and costs $20$ dollars per month. For how many months of membership will the total cost of both plans be exactly the same?

Answer: 6 months

Answer

The plans will cost the exact same amount at 6 months.

Setting the cost of Plan A (

45 + 30m

) equal to the cost of Plan B (

105 + 20m

) creates the equation

45 + 30m = 105 + 20m

. By isolating the variable, we find that

10m = 60

, which simplifies to

m = 6

. Therefore, it takes exactly

6

months for both memberships to cost the same.

Step-by-Step Solution

Define the variable and formulate a one-variable linear equation.

45 + 30m = 105 + 20m

To determine when the total costs are equal, the cost expression for Plan A (

45

fee plus

30

per month) must be set equal to the cost expression for Plan B (

105

fee plus

20

per month).

Subtract

20m

from both sides of the equation.

45 + 10m = 105

This groups all terms containing the variable

m

on one side of the equation.

Subtract

45

from both sides of the equation.

10m = 60

This isolates the variable term by moving all constant values to the opposite side of the equation.

Divide both sides by

10

m = 6

Dividing by the coefficient of the variable provides the final numerical solution for the unknown.

Key Concept

Translating a real-world scenario into a one-variable linear equation and isolating the variable to solve for an unknown value.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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