Question

1. a grade 8 class is selling bags of popcorn as a fundraiser. they spend $40 on popcorn kernels and toppings, popping - machine rental, and bags. they plan to sell bags of popcorn for $1.25 each. the profit they make will be equal to the money raised from sales minus the amount spent on supplies. (thinking) (application) (communication) a) write a linear equation to show how much profit they will make when they sell x bags of popcorn. explain how you developed the equation. b) how many bags of popcorn must they sell to pay for the supplies they bought?

Explanation:

Step1: Define variables and profit formula

Let $x$ be the number of bags of popcorn sold. The money raised from sales is $1.25x$ (since each bag is sold for $1.25$). The cost of supplies is $40$. The profit $P$ is given by the formula $P = \text{Revenue}-\text{Cost}$. So, $P=1.25x - 40$.

Step2: Find number of bags to break - even

To pay for the supplies (i.e., break - even where profit $P = 0$), we set $P=0$ in the equation $P = 1.25x-40$. Then $0=1.25x - 40$. Add $40$ to both sides: $40 = 1.25x$. Divide both sides by $1.25$: $x=\frac{40}{1.25}=32$.

Answer:

a) The linear equation is $P = 1.25x-40$, where $P$ is the profit and $x$ is the number of bags of popcorn sold. The equation is developed from the profit formula $P=\text{Revenue}-\text{Cost}$, with revenue from selling $x$ bags at $1.25$ each and cost of $40$ for supplies.
b) They must sell 32 bags of popcorn to pay for the supplies.