Question

Jason goes to the local butcher shop to buy wings (y) and hot dogs (x) for a superbowl Sunday party with friends. He can get 10 wings for $0.50 each with a purchase of 2 dozen or more and hot dogs for $1.00 each with a purchase of 10 or more. He budgeted $40 for food at the party.

1) write a system of three inequalities that models this situation

2) if Jason buys 24 wings, what is the maximum number of hot dogs that he can buy? Show work

3) what is the
Jason goes to the local butcher shop to buy wings (y) and hot dogs (x) for a superbowl Sunday party with friends. He can get 10 wings for $0.50 each with a purchase of 2 dozen or more and hot dogs for $1.00 each with a purchase of 10 or more. He budgeted $40 for food at the party.

1) write a system of three inequalities that models this situation

2) if Jason buys 24 wings, what is the maximum number of hot dogs that he can buy? Show work

3) what is the maximum number of wings that Jason can buy?

4) can Jason Buy 30 Hot Dogs?

5) if Jason buys 20 hot dogs. How many wings can he buym

6) if Jason buys 50 wings. How many hot dogs can he buy?

Answer 1

1. System of inequalities:10y≤0.50x

x≥10

0.50x+y≤40

2. If Jason buys 24 wings, the maximum number of hot dogs (x) he can buy is 60. (Work: 10y≤0.50(24)→10y≤12→y≤1.2, and since x≥10, x can be maximized at 60).

3. The maximum number of wings (y) that Jason can buy is 96.

4. No, Jason cannot buy 30 hot dogs because the minimum cost for 30 hot dogs is $30, exceeding his $40 budget.

5. If Jason buys 20 hot dogs, he can buy 10 wings.

6. If Jason buys 50 wings, he can buy 5 hot dogs.

The system of three inequalities models Jason's situation. The first inequality, 10y≤0.50x, represents the cost of purchasing wings at $0.50 each. The second inequality, x≥10, indicates that Jason must purchase at least 10 hot dogs to qualify for the $1.00 each price. The third inequality, 0.50x+y≤40, represents Jason's budget constraint of $40.

If Jason buys 24 wings, the maximum number of hot dogs he can buy is 60. This is determined by the cost constraint (10y≤0.50(24)) and the requirement to purchase at least 10 hot dogs (x≥10).

The maximum number of wings Jason can buy is 96. This is found by solving the budget constraint 0.50x+y≤40 while considering the other inequalities.

Jason cannot buy 30 hot dogs because the cost constraint x≥10 makes the minimum cost for 30 hot dogs exceed his $40 budget.

If Jason buys 20 hot dogs, he can buy 10 wings. This is determined by satisfying the cost constraint 0.50x+y≤40 while considering the other inequalities.

If Jason buys 50 wings, he can buy 5 hot dogs. This is determined by satisfying the cost constraint 0.50x+y≤40 while considering the other inequalities.