(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 $m\ge 2$.

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: $1.25m=1.50(m-2)$

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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.