(a)

Question

Part A
Kiera's monthly magazine subscription costs $1.25 per issue. Tiauna's monthly subscription costs $1.50 per issue but she received her first 2 issues free. Which equation can be used to find the number of months after which the girls will have paid the same amount?


A
1.25m=1.50m−2

B
1.25m=1.50m−2m

C
1.25m=1.50(m−2)

D
1.25m=3m−1.50

(b)


Part B

After how many months did the girls pay the same amount?

After

months.

Answer 1

To solve Part A, we want to find the equation that represents the situation where Kiera and Tiauna have paid the same amount after a certain number of months.

Kiera's cost after \( m \) months is:

• \( 1.25m \)

Tiauna's cost after \( m \) months is:

• She gets her first 2 issues free, so after 1 month, she pays $1.50. After 2 months she pays $1.50 × 2, but the first two issues are free, so starting from the third month, she pays for the remaining months:
• Her cost after \( m \) months will be \( 1.50(m - 2) \) for \( m \geq 2 \).

Thus, the equation to find when they paid the same is: \[ 1.25m = 1.50(m - 2) \]

So the correct answer for Part A is: C: \( 1.25m = 1.50(m - 2) \)

---

For Part B, we'll solve the equation \( 1.25m = 1.50(m - 2) \):

1. Expand the right side: \[ 1.25m = 1.50m - 3.00 \]

2. Rearrange the equation: \[ 1.25m - 1.50m = -3.00 \] \[ -0.25m = -3.00 \]

3. Divide both sides by -0.25: \[ m = \frac{-3.00}{-0.25} = 12 \]

Therefore, after 12 months, the girls will have paid the same amount.

In summary:

• Part A: C
• Part B: 12 months.