Question

2) Your class is raising money for a class trip. You make $10 on each pizza and $4 on each box of cookies that you sell.

How many items of each type must you sell to raise more than $100? Write and graph an inequality to model the
situation. Define the variables and state the constraints. Give three possible combinations that you could sell.

Answer 1

The variables are 'p' and 'c'.

The inequality is:
`10p+4c\geq100`

The graph is plotted below.

Three possible solutions are: (0, 25), (10, 0) and (5, 20)

Explanation:

Let the number of pizzas sold be 'p' and number of cookies sold be 'c'.

Given:

Price per pizza = $10

Price per cookie = $4

Minimum amount to be earned = $100

Price for 'p' pizzas sold =
`10p`

Price for 'c' cookies sold =
`4c`

As per question:

`10p+4c\geq100`

Also, number of pizzas and cookies can't be negative. So,

`p\geq0,c\geq0`

Plotting the above inequalities on a graph using DESMOS.

The region that is common to all the above inequalities is the solution region and is shown in the graph below.

The solution region also includes all the points on the line.

So, the three possible combinations of solutions can be any 3 points in the solution region. One such combination is:

(0, 25), (10, 0) and (5, 20)