Meredith runs the souvenir store for a minor-league baseball team. She checked into how much it would cost to have smartphone cases made that feature an image of the team’s mascot. One manufacturer charges a $250 fee to design and print the personalized cases, plus the cost of the actual cases. The first 50 cases cost $5 each, and the next 100 cases cost $3 each. Write an equation to determine how many cases Meredith can purchase with a budget of $750. Determine the constraints on the terms of the equation based on the situation, then apply the constraints to solve for the number of cases that can be purchased.

Write an equation in words for determining the total cost to produce the personalized cases.

Write an equation for the cost of cases if is 50 or less.

Write an equation for the cost if is the number of cases that are $5 each and is the number of cases that are $3 each.

List any constraints on the value of the expression .

Write an equation for the amount of money Meredith has available to spend as a function of the cost equation identified in step 3.

List any constraints on the terms on the right side of the resulting equation.

Substitute this constraint into the equation from step 5 and simplify.

Apply any remaining constraints to the value of and determine the total number of cases Meredith can purchase for $750.

This applet is provided by Walch Education as supplemental material for the UCSS Secondary Math III program. Visit www.walch.com for more information on our resources.