Question

At the deli counter in the supermarket, Nigel paid $10 for 212 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?
y=__x

Answer 1

wrong

Answer 2

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?

Answer 3

At the deli counter in the supermarket, Nigel paid $10 for 212 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?
y=__x

Answer 4

To find the equation representing the proportional relationship between the cost of deli meat and its weight, we start by representing the cost as \(y\) and the weight in pounds as \(x\).

Given that Nigel paid $10 for 2 pounds of roast beef, we can express this relationship as:

\[
y = kx
\]

where \(k\) is the constant of proportionality (the cost per pound).

To find \(k\), we use the given information:

\[
10 = k \cdot 2
\]

Solving for \(k\):

\[
k = \frac{10}{2} = 5
\]

Now we can write the equation that represents the cost of the roast beef:

\[
y = 5x
\]

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

\[
y = 5x
\]

Answer 5

I apologize for the mistake in my previous response. Let's clarify the problem correctly.

Nigel paid $10 for 2 pounds of roast beef, not 212 pounds. Let’s write the correct relationship based on the information provided:

1. He paid $10 for \(2\) pounds of roast beef.
2. The cost \(y\) is proportional to the weight \(x\).

To find the constant of proportionality \(k\):

Given that \(y = kx\),
\[
10 = k \cdot 2
\]

Now, solving for \(k\) gives:

\[
k = \frac{10}{2} = 5
\]

So the equation should be:

\[
y = 5x
\]

This equation means that for each pound of roast beef, the cost is $5.

If we mistakenly interpreted the weight as 212 pounds instead of 2, I apologize for that confusion. If Nigel indeed paid $10 for approximately 212 pounds, we should correct the calculations accordingly:

Using the original weights provided:
Given \(y = 10\) when \(x = 212\):
\[
y = kx \implies 10 = k \cdot 212
\]
Solving for \(k\):
\[
k = \frac{10}{212} \approx 0.04717
\]

So if you are referring to 212 pounds, the equation would be:

\[
y \approx 0.04717x
\]

Please let me know which scenario you were referring to, either the 2 pounds or the 212 pounds, for further clarification or corrections. Thank you!

Answer 6

Thank you for the clarification. If Nigel paid $10 for \(2 \frac{1}{2}\) pounds of roast beef, we need to first convert \(2 \frac{1}{2}\) into an improper fraction or a decimal.

Converting \(2 \frac{1}{2}\) pounds to a decimal:

\[
2 \frac{1}{2} = 2.5 \text{ pounds}
\]

Since the cost \(y\) is proportional to the weight \(x\), we can write the equation in the form:

\[
y = kx
\]

where \(k\) is the constant of proportionality (the cost per pound).

To find \(k\):

Given that:

\[
y = 10 \quad \text{when} \quad x = 2.5
\]

We can substitute these values into the equation:

\[
10 = k \cdot 2.5
\]

Now, solving for \(k\):

\[
k = \frac{10}{2.5} = 4
\]

Now that we have \(k\), we can write the equation that represents the cost of the roast beef:

\[
y = 4x
\]

This means that the cost per pound of roast beef is $4.

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

\[
y = 4x
\]

Answer 7

To find the equation that represents the proportional relationship between the cost and weight of the roast beef, we can follow these steps:

1. **Identify Variables**:
- Let \( y \) be the cost in dollars.
- Let \( x \) be the weight in pounds.

2. **Given Information**:
- Nigel paid $10 for 212 pounds of roast beef.

3. **Proportional Relationship**:
The cost is proportional to the weight, meaning we can express this relationship with the equation:
\[
y = kx
\]
where \( k \) is the constant of proportionality (the cost per pound).

4. **Finding \( k \)**:
We can find \( k \) using the information provided:
\[
10 = k \cdot 212
\]

To solve for \( k \):
\[
k = \frac{10}{212}
\]

Now, simplify:
\[
k = \frac{10}{212} \approx 0.04717
\]
(You can also express it as a fraction: \( k = \frac{5}{106} \)).

5. **Final Equation**:
Now we can write the equation for the cost as:
\[
y = \frac{10}{212}x \quad \text{or} \quad y \approx 0.04717x
\]

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

\[
y = \frac{10}{212}x
\]

Alternatively, you can express it as \( y \approx 0.04717x \).