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?
Let's assume the weight of deli meat is represented by the variable w and the cost of deli meat is represented by the variable c.
We are given that Nigel paid $10 for 2 1/2 pounds, which can be written as 2.5 pounds.
According to the given information, the cost of deli meat is proportional to its weight. This means that the cost is equal to a constant multiple of the weight. Let's call this constant multiple k.
So we can write the equation as:
c = k * w
We need to find the value of k. For that, we can use the given information that Nigel paid $10 for 2.5 pounds.
Substituting c = 10 and w = 2.5 into the equation, we have:
10 = k * 2.5
Dividing both sides of the equation by 2.5, we get:
k = 10 / 2.5
k = 4
Now that we have the value of k, we can write the equation of the proportional relationship as:
c = 4w.
To find the equation for the graph of this proportional relationship, we need to determine the constant of proportionality, which represents the cost per pound of roast beef.
Let's denote the cost of the roast beef as C and the weight in pounds as w.
We know that Nigel paid $10 for 2 1/2 pounds of roast beef. So, we can set up the following proportion:
C / w = 10 / (2 1/2)
Let's convert 2 1/2 pounds to an improper fraction:
C / w = 10 / (5/2)
To divide by a fraction, we multiply by its reciprocal:
C / w = 10 * (2/5)
Simplifying the right side:
C / w = 20/5
C / w = 4
Now we have the equation for the proportional relationship:
C = 4w
Therefore, the equation for the graph of this proportional relationship is C = 4w, where C represents the cost and w represents the weight in pounds.
To find the equation for the graph of this proportional relationship, we need to analyze the information given.
We know that Nigel paid $10 for 2 1/2 pounds of roast beef. This means that the cost of the deli meat is proportional to its weight. In other words, the cost per pound is constant.
Let's define some variables:
- Let x represent the weight of the roast beef in pounds.
- Let y represent the cost of the roast beef in dollars.
Now, we can set up a proportion based on the given information:
x pounds / y dollars = 2 1/2 pounds / $10
To simplify the given fraction, we convert 2 1/2 to an improper fraction:
2 1/2 = (2 * 2 + 1) / 2 = 5 / 2
Our proportion now becomes:
x / y = 5 / 2
To get the equation for the graph, we can cross multiply:
2x = 5y
Now, rearrange the equation to solve for y:
y = (2x) / 5
The equation for the graph of this proportional relationship is:
y = (2/5)x