At the store, Nigel paid $10 for 2 1/2 pounds of roast beef. The cost of deli meat is proportional to it's weight. What is the equation for the graph of this proportional relationship?

Answer 1

Let's denote the cost of deli meat as C (in dollars) and the weight of the meat as W (in pounds). We are given that Nigel paid $10 for 2 1/2 pounds of roast beef. This can be written as:

C = 10

Since the cost of deli meat is proportional to its weight, we introduce a constant of proportionality, k:

C = kW

Combining these two equations, we have:

10 = k(2 1/2)

To simplify, we convert the mixed number 2 1/2 to an improper fraction:

10 = k(5/2)

Multiplying both sides by 2/5 to isolate k, we get:

k = 10 * (2/5) = 20/5 = 4

Thus, the equation for the graph of this proportional relationship is:

C = 4W