Question

select the correct answer.

a pizza restaurant starts the day with a certain amount of pizza dough. the length of time the dough will last varies inversely with the number of medium pizzas made.

if they need to make 32 medium pizzas, the dough will last 5 hours. how long will the dough last if they need to make 40 pizzas?

2.75 hours
4 hours
8 hours
6.25 hours

Explanation:

Set up the inverse variation equation

The problem states that the length of time the dough will last, \(t\), varies inversely with the number of medium pizzas made, \(p\). This relationship is represented by the formula:

$$t = \frac{k}{p}$$

where \(k\) is the constant of variation.

Find the constant of variation

We are given that if they make \(p = 32\) medium pizzas, the dough will last \(t = 5\) hours. We substitute these values into our equation to solve for \(k\):

$$5 = \frac{k}{32}$$

$$k = 5 \times 32 = 160$$

Calculate the time for the new scenario

Now we need to find how long the dough will last, \(t\), if they make \(p = 40\) pizzas. Using our constant \(k = 160\):

$$t = \frac{160}{40}$$

$$t = 4$$

The dough will last \(4\) hours.

Answer:

• 2.75 hours
• 4 hours (Correct answer)
• 8 hours
• 6.25 hours