Question

You invited 17 people to your house for a party. You want to spend a $50 gift card completely on the items shown. You also want to have exactly two servings of food for each person. A pizza is $6 for 4 servings, and a bag of chicken wings costs $7 for 5 servings. Write a system of linear equations that represents the situation.

Answer 1

6p + 7c = 50

4p + 5c = 34

(where p is the number of pizzas and c is the number of bags of chicken wings)

We need to buy 6 pizzas and 2 bags of chicken wings in order to spend a total of $50, AND for each of the 17 people to have 2 servings of food.

Explanation:

Let p = number of pizzas

Let c = number of bags of chicken wings

Equation 1

Given:

• Pizza = $6
• Bag of chicken wings = $7
• Total spend = $50

⇒ 6p + 7c = 50

Equation 2

Given:

• Pizza = 4 servings
• Chicken wings = 5 servings
• Total servings needed = 17 × 2 = 34

⇒ 4p + 5c = 34

Equation 3

Multiply Equation 2 by 1.5:

⇒ 6p + 7.5c = 51

Subtract Equation 1 from Equation 3 and solve for c:

⇒ 0.5c = 1

⇒ c = 2

Substitute found value of c into Equation 2 and solve for p:

⇒ 4p + 5(2) = 34

⇒ 4p + 10 = 34

⇒ 4p = 24

⇒ p = 6

Therefore, we need to buy 6 pizzas and 2 bags of chicken wings in order to spend a total of $50, AND for each of the 17 people to have 2 servings of food.