Questions: The graph shows the cost C in dollars of w pounds of peanuts, a proportional relationship. Select all the statements A. 2.5 pounds of peanuts costs 1. B. 1 pound of peanuts costs 2.50. C. 5 pounds of peanuts cost 12.50. D. 0.9 pound of peanuts cost 19.50. E. The point (4,10) is on the graph of the proportional relationship.

The graph shows the cost C in dollars of w pounds of peanuts, a proportional relationship. Select all the statements
A. 2.5 pounds of peanuts costs 1.
B. 1 pound of peanuts costs 2.50.
C. 5 pounds of peanuts cost 12.50.
D. 0.9 pound of peanuts cost 19.50.
E. The point (4,10) is on the graph of the proportional relationship.

Transcript text: The graph shows the cost Cin datisers of w paunds of peanuts, a prepartional relatianselp. select all the the statamente A. 2.5 pounds of peamuts costs $\$ 1$. B. 1 pound of pranuts casts $\$ 2.50$. C. 5 pounds of poanuts cost $\$ 12.50$. 0.9 pousde of pranuts cost $\$ 19.50$ E. The point $(4,10)$ is on the graph of the proportional rolationship.

Solution

Solution Steps

Step 1: Find the constant of proportionality

The graph passes through the point (7, 17.5). This means that 7 pounds of peanuts costs $17.50. To find the cost per pound (the constant of proportionality), divide the cost by the number of pounds: 17.50 / 7 = 2.50. Thus, the constant of proportionality is 2.5, meaning 1 pound of peanuts costs $2.50.

Step 2: Evaluate option A

2.5 pounds of peanuts costs 2.5 * $2.50 = $6.25. Option A states that 2.5 pounds of peanuts costs $1, which is false.

Step 3: Evaluate option B

From Step 1, we found that 1 pound of peanuts costs $2.50, which means option B is true.