To determine which bag of dog food is the better buy, we need to calculate the unit price (price per kilogram) for each bag and then compare these unit prices.
1. Calculate the unit price for the [tex]$6.35$[/tex]-kg bag:
[tex]\[
\text{Unit Price} = \frac{\text{Total Cost}}{\text{Weight}} = \frac{\$12.98}{6.35 \, \text{kg}}
\][/tex]
[tex]\[
\text{Unit Price} = \frac{12.98}{6.35} \approx 2.04
\][/tex]
So, the unit price for the [tex]$6.35$[/tex]-kg bag is \$2.04 per kg, rounded to the nearest cent.
[tex]\[
\text{Unit price for the } 6.35\text{-kg bag: } \$2.04 \, \text{per kg}
\][/tex]
2. Calculate the unit price for the [tex]$7.03$[/tex]-kg bag:
[tex]\[
\text{Unit Price} = \frac{\text{Total Cost}}{\text{Weight}} = \frac{\$14.88}{7.03 \, \text{kg}}
\][/tex]
[tex]\[
\text{Unit Price} = \frac{14.88}{7.03} \approx 2.12
\][/tex]
So, the unit price for the [tex]$7.03$[/tex]-kg bag is \$2.12 per kg, rounded to the nearest cent.
[tex]\[
\text{Unit price for the } 7.03\text{-kg bag: } \$2.12 \, \text{per kg}
\][/tex]
3. Compare the unit prices to determine which bag is the better buy:
- The unit price of the [tex]$6.35$[/tex]-kg bag is \$2.04 per kg.
- The unit price of the [tex]$7.03$[/tex]-kg bag is \$2.12 per kg.
Since \[tex]$2.04 per kg is less than \$[/tex]2.12 per kg, the [tex]$6.35$[/tex]-kg bag is the better buy.
[tex]\[
\text{The better buy: The } 6.35\text{-kg bag}
\][/tex]
Thus, the completed answers are:
[tex]\[
\text{Unit price for the } 6.35\text{-kg bag: } 2.04 \, \text{\$ per kg}
\][/tex]
[tex]\[
\text{Unit price for the } 7.03\text{-kg bag: } 2.12 \, \text{\$ per kg}
\][/tex]
The better buy:
[tex]\[
\text{The } 6.35\text{-kg bag}
\][/tex]
