# Example 1

- Author:
- Walch Education

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.