At the deli counter in the supermarket Nigel paid $10 for 21/2 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

Question

At the deli counter in the supermarket Nigel paid $10 for 21/2 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

Answer 1

Let's assume that x represents the weight of the deli meat in pounds and y represents the cost of the deli meat in dollars.

We know that Nigel paid $10 for 21/2 pounds of roast beef, which can be written as:
10 = (2 1/2)x

To simplify the equation, we can convert 2 1/2 to an improper fraction:
10 = 5/2 * x

Now, let's isolate x by dividing both sides of the equation by 5/2:
10 / (5/2) = x

To divide by a fraction, we need to multiply by its reciprocal:
10 * (2/5) = x
4 = x

Therefore, the equation for the graph of this proportional relationship is:
y = 4x

Answer 2

To find the equation for the graph of this proportional relationship, we need to determine the rate at which the cost of deli meat changes with respect to its weight.

Let's assume the cost of deli meat (C) is proportional to its weight (W). The constant of proportionality will be denoted by k.

Therefore, the equation for this relationship can be written as:

C = kW

To find the value of k, we can use the information given in the problem. Nigel paid $10 for 2 1/2 pounds of roast beef, which can also be written as 2.5 pounds.

Substituting the values into the equation:

10 = k * 2.5

To solve for k, divide both sides of the equation by 2.5:

k = 10 / 2.5

Simplifying the expression:

k = 4

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

C = 4W

Answer 3

To find the equation for the graph of this proportional relationship, we can use the formula for proportionality, which states that the ratio between two variables is constant. In this case, the cost of the deli meat is proportional to its weight.

Let's denote the cost of the deli meat as "C" and the weight of the deli meat as "W".

From the given information, we know that when Nigel bought 2 1/2 pounds of roast beef, he paid $10.

To find the constant of proportionality, we can set up a proportion:

C/W = 10/(2 1/2)

To simplify the right side, we need to convert the mixed fraction into an improper fraction:

2 1/2 = (2 * 2 + 1) / 2 = 5/2

So the proportion becomes:

C/W = 10 / (5/2)

To divide by a fraction, we can multiply by its reciprocal:

C/W = 10 * (2/5)

Simplifying further:

C/W = 4/1

Now, we have the equation for the graph of this proportional relationship:

C = (4/1)W

Simplifying, we get:

C = 4W

Therefore, the equation for the graph of this proportional relationship is C = 4W, where C represents the cost of the deli meat and W represents its weight.