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.
It's not the size of the box that makes a better buy, it is the quantity and quality of the contents.
Are all edges of the boxes the same ratio or only one edge?
2/3 = .67
$2.50/$4.00 = .625
I hope this helps. Thanks for asking.
I think the assumption we were supposed to make that the volume of two similar solids is proportional to the cubes of their sides.
the ratio of their sides is 2:3
so the ratio of their cubes is 8:27
So if they were priced by the same unit price, the larger should cost 27/8($2.50)
= $8.44
but the larger only costs $4.00, so buyer the larger box is definitely a much better deal.
To determine which cereal box is the better buy, we need to compare the prices per square unit of the two boxes. However, since the problem does not provide any information about the sizes of the boxes or their dimensions, we need to make the assumption that the ratio of corresponding edges also applies to the areas of the boxes.
To solve this problem, we can follow these steps:
1. Determine the ratio of the prices for the two cereal boxes: $2.50 for the smaller box and $4.00 for the larger box.
2. Compare the corresponding edges ratio of 2:3 with the assumption that it applies to the areas as well. This means that the ratio of the areas between the smaller and larger box is also 2:3.
3. Calculate the area of the smaller box by squaring the ratio (2) and multiplying it by the base area. Let's say the base area of the smaller box is A:
Area of the smaller box = A * (2^2) = 4A
4. Calculate the area of the larger box using the corresponding ratio:
Area of the larger box = A * (3^2) = 9A
5. Compare the prices per unit area of the two boxes:
Price per unit area of the smaller box = Cost of the smaller box / Area of the smaller box
Price per unit area of the larger box = Cost of the larger box / Area of the larger box
6. Compute the estimates of the prices per unit area using the given prices:
Estimated price per unit area of the smaller box = $2.50 / 4A
Estimated price per unit area of the larger box = $4.00 / 9A
7. Simplify the price per unit area expressions by dividing the numerator and denominator by A:
Estimated price per unit area of the smaller box = $2.50 / 4
Estimated price per unit area of the larger box = $4.00 / 9
8. Compare the estimated prices per unit area to determine which box is the better buy. The better buy will be the cereal box with the lower estimated price per unit area.
By calculating the estimated price per unit area for both boxes, we can determine which one is the better buy.