Question

One health club charges a 44 sign-up fee and 30 per month. A second health club charges a 99 sign-up fee and 25 per month. For what number of months is the cost of the first health club no more than the cost of the second health club?

Answer 1

To compare the cost of two health clubs, set up equations for each club's cost and solve the inequality. The cost of the first health club is no more than the cost of the second health club for a maximum of 11 months.

Step-by-step explanation:

To compare the cost of the two health clubs, we need to set up an equation.

The cost of the first health club is given by the equation C1 = 44 + 30m, where m is the number of months.

The cost of the second health club is given by the equation C2 = 99 + 25m.

To find the number of months for which the cost of the first health club is no more than the cost of the second health club, we need to solve the inequality C1 ≤ C2.

Substituting the equations for C1 and C2, we get 44 + 30m ≤ 99 + 25m.

Now, let's solve this inequality:

1. Subtract 25m from both sides: 44 + 5m ≤ 99.
2. Subtract 44 from both sides: 5m ≤ 55.
3. Divide both sides by 5: m ≤ 11.

The cost of the first health club is no more than the cost of the second health club for a maximum of 11 months.