Question

3.1. Complete the tables below: Situation Reasoning Number sentence Jim and Jabu each join a gym. Jim’s gym takes R150 deposit, and he pays R120 monthly. Jabu’s gym takes no deposit, but his monthly payment is R150. They compare their total payments after four months, after five months and after six months.

3.1.1 Reasoning

3.1.2 Number sentence

Answer 1

3.1.1 Reasonong

Jim’s gym takes R150 deposit, Jabu’s gym takes no deposit.

But Jim pays R120 monthly and Jabu’s monthly payment is R150.

Since $120<150,$ then there exists the time (some number of months $n_1$), when the total Jim’s payment for $n<n_1$ months is greater than Jabu’s payment for $n<n_1$ months.

The total Jim’s payment for $n_1$ months will be equal to the Jabu’s payment for $n_1$ months.

After that the total Jim’s payment for $n>n_1$ months will be than Jabu’s payment for $n>n_1$ months.

Since Jim’s gym takes R150 deposit, and he pays R120 monthly, then the total Jim’s payment for $n$ months is

$$A_{Jim}(n)=150+120n, n\geq0$$

Since Jabu’s gym takes no deposit, and he pays R150 monthly, then the total Jabu’s payment for $n$ months is

$$A_{Jabu}(n)=150n, n\geq0$$

They compare their total payments after four months, after five months and after six months.

3.1.2 Number sentence

$$A_{Jim}(4)=150+120(4)=630$$

$$A_{Jabu}(4)=150(4)=600$$

$$A_{Jim}(4)=630>600=A_{Jabu}(4)$$

$$A_{Jim}(5)=150+120(5)=750$$

$$A_{Jabu}(5)=150(5)=750$$

$$A_{Jim}(5)=750=A_{Jabu}(5)$$

$$A_{Jim}(6)=150+120(6)=870$$

$$A_{Jabu}(6)=150(6)=900$$

$$A_{Jim}(6)=870<900=A_{Jabu}(6)$$