Question

Grace has $105 to buy a cake and pizza for her cousin’s birthday party. She knows she needs to set aside $25 for the cake, and the rest of the money she can spend on pizzas. Each pizza costs $9.25. How many pizzas can Grace afford to buy?

a.write and solve an inequality to answer the question

b. each pizza serves 4 people. if 22 people reply that they will attend the party, how many pizzas should grace buy? explain your reasoning.

im sorry its alot but this will help me lots

Answer 1

A. She can buy 8 pizzas; B. At least 6 pizzas.

Explanation:

Since Grace has $105, we can set our inequality to be less than or equal to that amount of money. We also know she needs to spend $25 on the cake no matter what. Assuming x is the amount of pizzas she can buy and each pizza costs $9.25, our inequality looks like this:

9.25x + 25 ≤ 105

To solve this inequality, we first subtract 25 from both sides, which gives us:

9.25x ≤ 80

Then we divide by 9.25 on both sides, giving us:

x ≤ 8.6486

Since Grace is only able to buy whole pizzas, the most she can buy is 8 pizzas.

If each pizza serves 4 people and there are 22 people attending, we need to be able to feed 22 or more people. We can use this inequality, where x is still the number of pizzas.

4x ≥ 22

Dividing both sides by 4, we get:

x ≥ 5.5

Again, assuming we can only buy whole pizzas, we would need at least 6 pizzas to feed the entire party.