Question

At the daily counter in the supermarket natural paid $10 for two and a half pounds of roast beef the cost of the daily meat is proportional to its way what is the equation for the graph of this proportional relationship

Answer 1

To find the equation representing the proportional relationship between the cost of roast beef and its weight, we start by using the information given:

- Natural paid $10 for 2.5 pounds of roast beef.

We can set up the relationship as follows:

1. Let \( C \) represent the cost (in dollars).
2. Let \( W \) represent the weight (in pounds).
3. The problem states that the cost is proportional to the weight, which can be written in the form:
\[
C = kW
\]
where \( k \) is the constant of proportionality (price per pound).

Next, we need to find the value of \( k \):
- We know \( C = 10 \) when \( W = 2.5 \).

From the equation:
\[
10 = k \times 2.5
\]

To solve for \( k \):
\[
k = \frac{10}{2.5} = 4
\]

Now that we have determined \( k \), we can write the equation that describes the relationship:
\[
C = 4W
\]

This equation states that the cost \( C \) in dollars is 4 times the weight \( W \) of the roast beef in pounds.