two cereal boxes 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.
assumption: The cost of the cereal should be directly proportional to the volume.
volume(smaller):volume(larger) = 2^3:3^3 = 8:27
Let the volume of the smaller be 8x units
let the volume of the larger be 27x units
unit cost of smaller box = 2.5/(8x)
= .3125/x
unit cost of larger box = 4/27x
= .148/x
clearly the larger box is the better buy.
To determine which cereal box is the better buy, we need to compare the prices per unit of volume. Since the boxes have corresponding edges in a ratio of 2:3, we can assume that the volumes of the two boxes are also in a ratio of 2:3.
To solve this problem, let's define the volume of the smaller cereal box as V1 and the volume of the larger cereal box as V2. Since the volumes are in a ratio of 2:3, we can express this as:
V1 : V2 = 2 : 3
Let's assume the volume of the smaller cereal box is 2x (where x represents an arbitrary unit of volume). Then, the volume of the larger cereal box would be 3x.
Now, let's compare the prices per unit of volume. The price per unit of volume of the smaller box is $2.50 / V1 and the price per unit of volume of the larger box is $4.00 / V2.
Substituting the assumed values:
For the smaller box, price per unit of volume = $2.50 / (2x) = $1.25 / x
For the larger box, price per unit of volume = $4.00 / (3x) = $1.33 / x
To determine which box is the better buy, we need to compare the price per unit of volume. In this case, the smaller box, priced at $1.25 / x, has a lower price per unit of volume compared to the larger box, priced at $1.33 / x.
Therefore, based on this comparison, the smaller box, priced at $2.50, is the better buy because it has a lower price per unit of volume.
Assumptions made in solving this problem:
1. The size of the cereal boxes is determined solely by the corresponding edges.
2. The ratio of the edges corresponds to the ratio of the volumes.
3. The prices provided for the smaller and larger boxes are accurate.
To estimate and check the result, you can verify the calculations using the actual volumes of the cereal boxes if available. If the actual volumes of the boxes are different from the assumed values, recalculating the price per unit of volume using the actual volumes will give a more accurate result.