Question

todd is about to adopt a dog and is researching the best dry dog foods. he has narrowed his list down to three bags from three different brands, but he wants to be sure he gets the most protein for his money. the table below provides information about each bag of dog food.

bag	weight	percent protein	price
b	34 lb.	50%	$42.99
c	50 lb.	32%	$41.99

considering the cost per pound of protein, put the bags in order from best value to worst value.

Explanation:

To determine the best value, we calculate the cost per pound of protein for each bag. The formula for cost per pound of protein is:
\[
\text{Cost per lb of protein} = \frac{\text{Price}}{\text{Weight} \times \text{Percent protein (decimal)}}
\]

Step 1: Calculate for Bag A

Weight = 18 lb, Percent protein = 46% = 0.46, Price = $31.99
Protein weight = \( 18 \times 0.46 = 8.28 \) lb
Cost per lb of protein = \( \frac{31.99}{8.28} \approx 3.86 \) dollars/lb

Step 2: Calculate for Bag B

Weight = 34 lb, Percent protein = 50% = 0.50, Price = $42.99
Protein weight = \( 34 \times 0.50 = 17 \) lb
Cost per lb of protein = \( \frac{42.99}{17} \approx 2.53 \) dollars/lb

Step 3: Calculate for Bag C

Weight = 50 lb, Percent protein = 32% = 0.32, Price = $41.99
Protein weight = \( 50 \times 0.32 = 16 \) lb
Cost per lb of protein = \( \frac{41.99}{16} \approx 2.62 \) dollars/lb

Step 4: Compare the values

• Bag B: ~$2.53/lb
• Bag C: ~$2.62/lb
• Bag A: ~$3.86/lb

Lower cost per pound of protein means better value. So the order from best to worst is Bag B, Bag C, Bag A.

Answer:

Best to worst value: Bag B, Bag C, Bag A