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 x be the weight of the deli meat in pounds and y be the cost of the deli meat in dollars.
Since the cost of the deli meat is proportional to its weight, we can write the equation as:
y = kx, where k is the constant of proportionality.
Given that Nigel paid $10 for 2 1/2 pounds of roast beef, we can substitute these values into the equation to find the value of k:
10 = k * 2.5
Divide both sides by 2.5:
k = 10/2.5 = 4
Therefore, the equation for the graph of this proportional relationship is:
y = 4x.
To find the equation for the graph of this proportional relationship, we can use the formula:
cost = rate * weight
In this case, we know that Nigel paid $10 for 2 1/2 pounds of roast beef. Let's convert 2 1/2 pounds to a decimal:
2 1/2 pounds = 2.5 pounds
We can substitute this information into the formula:
10 = rate * 2.5
Now, we can solve for the rate:
rate = 10 / 2.5
rate = 4
Therefore, the equation for the graph of this proportional relationship is:
cost = 4 * weight
To determine the equation for the graph of this proportional relationship, we can use the concept of unit rate.
The given information states that Nigel paid $10 for 2 1/2 pounds of roast beef. To find the unit rate, we need to determine the cost per pound. To do this, we divide the total cost by the total weight.
First, convert 2 1/2 pounds into a mixed number. Since 1/2 is equal to 0.5, then 2 1/2 pounds can be written as 2.5 pounds.
Now, we can find the unit rate by dividing $10 by 2.5 pounds:
Unit Rate = Total Cost ÷ Total Weight
Unit Rate = $10 ÷ 2.5 pounds
Simplifying the division, we find that the cost per pound is $4.
Therefore, the equation for the graph of this proportional relationship is:
Cost = Rate × Weight
In this case, the rate (or cost per pound) is $4, and the weight is represented as 'w'. So, the equation becomes:
Cost = $4w
This equation represents the graph of the proportional relationship between the cost of deli meat and its weight, where 'w' represents the weight in pounds and the cost is given in dollars.