Question

use polyas four - step method to solve the following problems.
a. which is the better value?
24 - ounce box of cereal for $4.51
15.3 - ounce box of cereal for $3.69
b. the supermarket displays the unit price for the 15.3 - ounce box in terms of cost per ounce, but displays the unit price for the 24 - ounce box in terms of cost per pound. what are the unit prices, to the nearest cent, given by the supermarket?
unit price for the 15.3 - ounce box: $ per ounce

Explanation:

Step1: Calculate unit price for 24-ounce box

To find the unit price (cost per ounce) for the 24-ounce box, we divide the total cost by the number of ounces. The formula for unit price \( p \) is \( p=\frac{\text{Total Cost}}{\text{Number of Ounces}} \). For the 24-ounce box, total cost is \$4.51 and number of ounces is 24. So, \( p_{24}=\frac{4.51}{24}\approx0.1879 \) dollars per ounce.

Step2: Calculate unit price for 15.3-ounce box

For the 15.3-ounce box, total cost is \$3.69 and number of ounces is 15.3. Using the same unit price formula, \( p_{15.3}=\frac{3.69}{15.3}\approx0.2412 \) dollars per ounce.

Step3: Compare unit prices (part a)

We compare \( p_{24}\approx0.1879 \) and \( p_{15.3}\approx0.2412 \). Since \( 0.1879<0.2412 \), the 24-ounce box has a lower unit price, so it is the better value.

Step4: Calculate unit price for 15.3-ounce (part b - per ounce)

We already calculated \( p_{15.3}=\frac{3.69}{15.3}\approx0.24 \) dollars per ounce (to the nearest cent).

Step5: Calculate unit price for 24-ounce (part b - per pound)

First, convert ounces to pounds. Since 1 pound = 16 ounces, 24 ounces \(=\frac{24}{16}=1.5\) pounds. The total cost is \$4.51. So unit price per pound LXI1 dollars per pound (to the nearest cent). And the unit price for 15.3-ounce box (per ounce) is approximately \$0.24 per ounce.

Answer:

a. The better value is the 24-ounce box of cereal for \$4.51.
b. Unit price for 15.3-ounce box: \$0.24 per ounce; Unit price for 24-ounce box (per pound): \$3.01 per pound.