A company sells cereal in two different-sized boxes: a 17-ounce box for $2.89, and a 24-ounce box for $3.29. How do the unit prices of the two boxes compare?

Question

The smaller box is the better buy because it is approximately 1.4 cents cheaper per ounce.
The smaller box is the better buy because it is approximately 3.3 cents cheaper per ounce.
The larger box is the better buy because it is approximately 1.4 cents cheaper per ounce.
The larger box is the better buy because it is approximately 3.3 cents cheaper per ounce.

Answer 1

To determine which box is the better buy based on unit prices (cents per ounce), we can calculate the unit price for each box.

1. For the 17-ounce box:

   • Price: $2.89
   • Unit price: \( \frac{2.89 \text{ dollars}}{17 \text{ ounces}} \)
   • First, convert the price to cents: 2.89 dollars = 289 cents.
   • Unit price: \( \frac{289 \text{ cents}}{17 \text{ ounces}} \approx 17 \text{ cents per ounce} \).

2. For the 24-ounce box:

   • Price: $3.29
   • Unit price: \( \frac{3.29 \text{ dollars}}{24 \text{ ounces}} \)
   • Convert the price to cents: 3.29 dollars = 329 cents.
   • Unit price: \( \frac{329 \text{ cents}}{24 \text{ ounces}} \approx 13.71 \text{ cents per ounce} \).

Now let's compare the unit prices:

• 17-ounce box: approximately 17 cents per ounce
• 24-ounce box: approximately 13.71 cents per ounce

The 24-ounce box has a lower unit price than the 17-ounce box.

To find out how much cheaper the larger box is per ounce, we can calculate the difference:

• Difference: \( 17 - 13.71 = 3.29 \) cents per ounce.

Thus, the correct answer is: The larger box is the better buy because it is approximately 3.3 cents cheaper per ounce.