Question

Proportional Relationships Quick Check

5 of 55 of 5 Items

Question
Use the image to answer the question.

Two price tags show the weight and cost of each bag. The first price tag shows a 2 pound bag, with a cost of 1 dollar and 99 cents, at 1 dollar per pound. The second price tag shows a 5 pound bag, with a cost of 3 dollars and 99 cents, at 0.80 cents per pound.

You have $10
to spend on carrots for your rabbits. Compare the prices for two different-sized bags. Which size is a better deal and why?

(1 point)
Responses

The 5-lb. bag is the better deal because it costs less than the 2-lb. bag.
The 5-lb. bag is the better deal because it costs less than the 2-lb. bag.

The 5-lb. bag is the better deal because the unit rate for the 5-lb. bag is less than the unit rate for the 2-lb. bag.
The 5-lb. bag is the better deal because the unit rate for the 5-lb. bag is less than the unit rate for the 2-lb. bag.

The 5-lb. bag is the better deal because 5 lb. is more than 2 lb.
The 5-lb. bag is the better deal because 5 lb. is more than 2 lb.

The 2-lb. bag is the better deal because it costs less.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

The 5-lb. bag is the better deal because the unit rate for the 5-lb. bag is less than the unit rate for the 2-lb. bag.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The correct response is: The 5-lb. bag is the better deal because the unit rate for the 5-lb. bag is less than the unit rate for the 2-lb. bag.

Explanation: To determine which size is a better deal, we need to compare the unit prices. The unit price is the cost per pound. In this case, the unit rate for the 2-lb. bag is 1 dollar per pound, while the unit rate for the 5-lb. bag is 0.80 cents per pound. Since the unit rate for the 5-lb. bag is less than the unit rate for the 2-lb. bag, the 5-lb. bag is the better deal.

Answer 3

[AI-generated answer — Explain Bot]

To compare prices and determine which size is a better deal, we need to calculate the unit rate for each bag. The unit rate is the cost per pound.

For the first price tag, we have a 2-pound bag with a cost of $1.99. Dividing the cost by the weight, we get a unit rate of $1.99 / 2 pounds = $0.995 per pound.

For the second price tag, we have a 5-pound bag with a cost of $3.99. Dividing the cost by the weight, we get a unit rate of $3.99 / 5 pounds = $0.798 per pound.

Now, with this information, let's analyze the answer choices:

- "The 5-lb. bag is the better deal because it costs less than the 2-lb. bag." This may seem like a reasonable answer, but we can't solely rely on the total cost of the bag to determine the better deal.

- "The 5-lb. bag is the better deal because the unit rate for the 5-lb. bag is less than the unit rate for the 2-lb. bag." This answer is correct. The unit rate for the 5-pound bag is $0.798 per pound, which is less than the unit rate for the 2-pound bag, which is $0.995 per pound. This means that for each pound of carrots, the 5-pound bag is cheaper.

- "The 5-lb. bag is the better deal because 5 lb. is more than 2 lb." This answer is incorrect. The weight of the bag alone does not determine the better deal. We need to compare the cost per pound.

- "The 2-lb. bag is the better deal because it costs less." This answer is incorrect. Although the 2-pound bag may have a lower total cost, we need to consider the unit rate to determine the better deal.

Based on the analysis above, the correct answer is "The 5-lb. bag is the better deal because the unit rate for the 5-lb. bag is less than the unit rate for the 2-lb. bag."