Solving Word Problem

Question

The WJ soccer team is having a fundraiser selling pizzas and soda. They will sell the pizza for $3 a slice and the soda for $2 each. They need to make at least 300 dollars. They will not sell more than 100 items.

a. Define the variables.

b.What are the constraints.

c. Write an inequality representing the number of items the team can sell.

d. write and inequality representing how much money they will make.

Answer 1

a. We can define the variables as follows:

P: number of pizzas sold

S: number of sodas sold

R: revenue (how much money the team makes)

b: There are two constraints. First, the team needs to make at least $300. The amount the team makes will equal the number of pizzas sold times $3 per pizza, plus the number of sodas sold times $2 per soda:

R=3P+2S

This must be greater than or equal to 300:

3P+2S ≥ 300

Second, the total number of items sold cannot exceed 100. We can write this as:

P+S ≤ 100

c. Same as second constraint above in anwer to (b)

d. Same as first inequality above in answer to (b). However, if we want to find out how many pizzas the team needs to sell to meet its revenue goal, let's first assume the team sells the maximum number of items, which is 100. That means that S = 100 - P. Then:

3P + 2(100-P) = 300

3P + 200 - 2P = 300

P = 100

So, to make $300 selling only 100 items, the team would have to sell 100 pizzas and no sodas.