Question

The souvenir shop at the ballpark sells signed baseballs for $2 each and signed miniature bats for$6 each. Jay can spend at most $12 to buy no more than 4 items. Create a system of inequalities to model this situation, and then graph the solution set. Which solution results in Jay spending all of his money to buy 4 items?

Answer 1

To create a system of inequalities, assign variables to represent the number of baseballs and miniature bats Jay buys. Graph the solution set by converting the inequalities into equations and identify the point where Jay spends all his money to buy 4 items.

Step-by-step explanation:

To create a system of inequalities to model this situation, we can assign variables to represent the number of baseballs and miniature bats Jay buys. Let x be the number of baseballs and y be the number of miniature bats. The total cost of the baseballs and bats should not exceed $12, so the first inequality is 2x + 6y ≤ 12. Additionally, Jay can buy at most 4 items, so the second inequality is x + y ≤ 4.

To graph the solution set, we can convert the inequalities into equations and graph the corresponding lines. The solution set will be the region that satisfies both inequalities. The solution that results in Jay spending all of his money to buy 4 items can be represented by a point on the line that represents x + y = 4, where both x and y are positive integers.