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.
Could someone show me how to solve this? I don't know what formulas to use.
what is 1/2 - 1/2
Im doing modeling subtraction of fractions
hint:
The volumes of the two similar boxes are proportional to the cubes of their corresponding sides.
so the larger box:smaller box = 27:8
so the larger holds over 3 times as much as the smaller.
Now look at the cost.
To solve this problem, first, we need to determine which cereal box is the better buy based on their prices and sizes.
Let's assume that the smaller cereal box has a length of 2x units and the larger cereal box has a length of 3x units. The ratio of their corresponding edges is given as 2:3.
Now, according to the problem, the cost of the smaller box is $2.50, and the cost of the larger box is $4.00. We need to determine which box provides more value for the price.
To solve this, we will analyze the cost per unit of length for each cereal box.
For the smaller box:
Cost per unit of length = Cost of the box / Length of the box
Cost per unit of length = $2.50 / (2x)
For the larger box:
Cost per unit of length = Cost of the box / Length of the box
Cost per unit of length = $4.00 / (3x)
Now, we need to compare the cost per unit of length for both boxes to determine which box is a better buy.
To estimate the better buy, we can choose an arbitrary value for x, such as x = 1. This will provide us with an estimated answer.
For the smaller box:
Cost per unit of length = $2.50 / (2 * 1) = $1.25/ unit
For the larger box:
Cost per unit of length = $4.00 / (3 * 1) = $1.33/ unit
Based on the estimates, the smaller box has a lower cost per unit of length, making it the better buy.
However, to confirm our estimate, let's check by calculating the actual cost per unit of length for both boxes.
Assuming the size ratio remains the same, and given that the smaller box costs $2.50:
Cost per unit of length = $2.50 / (2x)
And given that the larger box costs $4.00:
Cost per unit of length = $4.00 / (3x)
Now, we will compare the actual cost per unit of length for both boxes at x = 1:
For the smaller box:
Cost per unit of length = $2.50 / (2 * 1) => $2.50 / 2 => $1.25/ unit
For the larger box:
Cost per unit of length = $4.00 / (3 * 1) => $4.00 / 3 => $1.33/ unit
As we can see, the actual calculations match our estimates. The smaller box still has a lower cost per unit of length, making it the better buy based on the given information.
Assumptions made in this problem:
1. The ratio of the corresponding edges of the cereal boxes provided is accurate.
2. The cost of the cereal boxes is solely based on their size ratio, and there are no other factors involved in determining their prices.