The two cereal boxes shown have corresponding edges in a ratio of 2:3.If the smaller box sells for $2.50 and the larger box for $4.00, which is the better buy? Why? What assumption(s) do you have to make when solving

the problem? Estimate, then check.

I think the answer is the larger box, but when I tried taking the cost and dividing it by it's ratio, I got the large box is 1.33 and the small is 1.25. But I know that in Walmart, the larger box is always a better deal.

Help!

Condsider the volume ratio. If all three sides are in that ratio, then the volume ratio is (2:3)^3 or 8:27 that means the volume of the larger is 27/8=3.37 as much as the smaller.

multiply the 2.50 by 3.37 to get the equivalent price for the larger, but the larger is much less than this, so the larger is by far the best buy.

To determine which cereal box is the better buy, you need to compare the prices based on their ratio. Let's walk through the steps to arrive at the correct answer:

Step 1: Calculate the price per unit of measurement for each cereal box.
Since the given ratio is 2:3, we can assume that the ratio applies to the linear dimensions, such as length or width, of the cereal boxes. Let's assign variables to the dimensions, such as 2x and 3x, where x represents the common factor in the ratio.

Step 2: Set up a proportion to find the value of x.
We know that the smaller box sells for $2.50 and has corresponding edges in a ratio of 2:3. Thus, we can write the proportion:
2x / 3x = $2.50 / (unknown cost of larger box)
Simplifying this proportion, we get:
2 / 3 = $2.50 / (unknown cost of larger box)

Step 3: Solve for the unknown cost of the larger box.
To find the unknown cost of the larger box, we need to isolate the variable. Cross-multiplying the proportion, we get:
2 * (unknown cost of larger box) = 3 * $2.50
2 * (unknown cost of larger box) = $7.50
Dividing both sides by 2, we find:
(unknown cost of larger box) = $7.50 / 2
(unknown cost of larger box) = $3.75

So, the unknown cost of the larger box is $3.75.

Step 4: Compare the price per unit of measurement.
To find the price per unit of measurement, we divide the cost of each box by its corresponding dimension:
For the smaller box: $2.50 / (2x) = $1.25 / x
For the larger box: $3.75 / (3x) = $1.25 / x

We can see that the price per unit of measurement for both cereal boxes is the same: $1.25 / x.

Conclusion:
Based on the calculations, we find that the price per unit of measurement is the same for both the smaller and larger cereal boxes. Therefore, the assumption that the larger box is a better deal at Walmart does not hold in this scenario.

To confirm our estimation, we should now check the given prices of the boxes:
The smaller box costs $2.50, while the larger box costs $4.00.
Comparing the prices directly, we see that the smaller box is indeed the better buy since it is cheaper.

It's worth noting that the assumption made here is that the ratio of 2:3 applies to the linear dimensions of the cereal boxes. Additionally, we assumed that the price of the larger box was unknown, and we had to solve for it based on the given information.