Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a
$7.50 delivery fee and $14 per pizza. She wants to buy as many pizzas as she can, and she also needs to
keep the delivery fee plus the cost of the pizzas under $60.
Correct question: Jacque needs to buy some pizzas for a party at her office. She’s ordering from a restaurant that charges a $7.50 delivery fee and $14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60. Each pizza is cut into 8 slices, and she wonders how many total slices she can afford. What is the largest number of slices that Jacque can afford?
Answer: 7.50+14P<60.
Explanation: Let P represent the number of pizzas that Jacque buys. Given, delivery fee=$7.50; Per pizza cost=$14. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60, i.e. (delivery fee)+(Number of pizzas)*(Per pizza cost)<$60, i.e. 7.50 +14P<60. Required inequality: 7.50+14P<60.
If the restaurant fee is $7.5 and the price is $14 per pizza, she has $52.5 to spend on the pizzas after we deduct the restaurant fee.
That means she can get 52.5 / 14 = 3.75 pizzas.
Since she can't get .75 pizza, we can assume that she will order 3, which in total makes 8 x 3 = 24 slices.If she can however order 3.75 pizzas, .75 x 8 makes 6 slices so it is a total of 30 slices for 3.75 pizzas.
If the restaurant fee is $7.5 and the price is $14 per pizza, she has $52.5 to spend on the pizzas after we deduct the restaurant fee.
That means she can get 52.5 / 14 = 3.75 pizzas.
Since she can't get .75 pizza, we can assume that she will order 3, which in total makes 8 x 3 = 24 slices.If she can however order 3.75 pizzas, .75 x 8 makes 6 slices so it is a total of 30 slices for 3.75 pizzas.
1) First, we identify the correct inequality that represents the situation. The delivery fee is a set cost of $7.50, and each pizza has a cost of $14. The total cost, therefore, is expressed as the delivery fee plus the cost per pizza multiplied by the number of pizzas. Also, we know that the total cost cannot exceed $60. Therefore, the correct inequality is: $7.50 + $14P ≤ $60. This corresponds to Choice A.
2) To figure out how many pizzas Jacque can order, we need to solve the inequality for P.
$14P ≤ $60 - $7.50
$14P ≤ $52.50
P ≤ $52.50 / $14
Now, we divide $52.50 by $14 and we get approximately 3.75. As Jacque can't buy 0.75 of a pizza, she can afford to order only 3 pizzas.
3) Each pizza has 8 slices, so the total number of slices Jacque can afford is 3 pizzas times 8 slices per pizza, which equals 24 slices. So, Jacque can afford to provide 24 pizza slices for her party.
Now, I will double-check the process:
a) We determined the correct inequality that represents the situation: $7.50 + $14P ≤ $60.
b) We appropriately isolated P on one side of the inequality, which gave us P ≤ 3.75. Since we can't order 0.75 of a pizza, we round down to 3. This corresponds correctly with our initial mathematical model.
c) We calculated the total number of slices as 3 pizzas * 8 slices per pizza = 24 slices.
All steps check out correctly; therefore, it's safe to say that Jacque can afford to buy 3 pizzas yielding a total of 24 slices for her office party.
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