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Ratios, Proportions, and Percents

Computing Unit Prices to Find the Better Buy

Brian paid [tex]$\$[/tex]19.99[tex]$ for a $[/tex]7.98 \, \text{kg}[tex]$ bag of dog food. A few weeks later, he paid $[/tex]\[tex]$20.38$[/tex] for an [tex]$8.39 \, \text{kg}$[/tex] bag at a different store.

Find the unit price for each bag. Then state which bag is the better buy based on the unit price.

Round your answers to the nearest cent.

- Unit price for the [tex]$7.98 \, \text{kg}$[/tex] bag: [tex]$\$[/tex] \square \square[tex]$ per $[/tex]kg$
- Unit price for the [tex]$8.39 \, \text{kg}$[/tex] bag: [tex]$\$[/tex] \square \square[tex]$ per $[/tex]kg$

Which bag is the better buy?
A. The [tex]$7.98 \, \text{kg}$[/tex] bag
B. The [tex]$8.39 \, \text{kg}$[/tex] bag
C. Neither (They have the same unit price)

Sagot :

GinnyAnswer
To determine the unit price of each bag of dog food and find out which one is the better buy, we first need to compute the cost per kilogram for each bag. Then, we can compare these unit prices.

Step-by-Step Solution:

1. Calculate the unit price for the 7.98-kg bag:
- The price for this bag is $19.99.
- The weight of this bag is 7.98 kg.

To find the unit price, we divide the price by the weight:
[tex]\[ \text{Unit price for the 7.98-kg bag} = \frac{\[tex]$19.99}{7.98 \text{ kg}} \approx \$[/tex]2.51 \text{ per kg}
\][/tex]

2. Calculate the unit price for the 8.39-kg bag:
- The price for this bag is $20.38.
- The weight of this bag is 8.39 kg.

To find the unit price, we divide the price by the weight:
[tex]\[ \text{Unit price for the 8.39-kg bag} = \frac{\[tex]$20.38}{8.39 \text{ kg}} \approx \$[/tex]2.43 \text{ per kg}
\][/tex]

3. Compare the unit prices:
- The unit price for the 7.98-kg bag is approximately \$2.51 per kg.
- The unit price for the 8.39-kg bag is approximately \$2.43 per kg.

Since \[tex]$2.43 per kg is less than \$[/tex]2.51 per kg, the 8.39-kg bag has a lower unit price and thus is the better buy.

Results:
- Unit price for the 7.98-kg bag: \$2.51 per kg
- Unit price for the 8.39-kg bag: \$2.43 per kg
- The better buy: The 8.39-kg bag
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