Question

At the deli counter in the supermarket, Nigel paid $10 for 2 1/2 pounds of roast beef. The cost of deli meat is proportional to its weight. What is the equation for the graph of this proportional relationship?(1 point)

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Answer 1

To determine the equation for the proportional relationship between the cost of deli meat and its weight, we can start by identifying the variables:

Let \( C \) represent the cost in dollars and \( w \) represent the weight in pounds.

From the information provided, Nigel paid $10 for 2.5 pounds of roast beef. This gives us the following relationship:

\[
C = k \cdot w
\]

where \( k \) is the constant of proportionality (the cost per pound).

To find \( k \), we can use the given information:

\[
10 = k \cdot 2.5
\]

Now we can solve for \( k \):

\[
k = \frac{10}{2.5} = 4
\]

So the constant of proportionality \( k \) is 4, meaning the cost per pound is $4.

Now we can write the equation that models this relationship:

\[
C = 4w
\]

This equation shows that the cost \( C \) in dollars is equal to $4 times the weight \( w \) in pounds.