2. A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost \( \$ 12 \). How much will the caterer pay for the pasta there? a. Write a ratio for the given information about the cost of pasta. b. Would it be more helpful to write an equivalent ratio with 1 pound of pasta as one of the numbers, or with \( \$ 1 \) as one of the numbers? Explain your reasonins and then write that equivalent ratio. c. Find the answer and explain or show your reasoning.

Let's solve the problem step by step. ### Step 1: Extract Known Conditions - The caterer needs to buy 21 pounds of pasta. - The cost of 8 pounds of pasta is \( \$ 12 \). ### Step 2: Write a Ratio for the Given Information a. The ratio of the cost of pasta to the weight of pasta can be expressed as: \[ \text{Ratio} = \frac{\text{Cost}}{\text{Weight}} = \frac{12}{8} \] ### Step 3: Equivalent Ratio b. To find an equivalent ratio, it is often more helpful to express the cost per pound, as this will allow us to easily calculate the total cost for any amount of pasta. Therefore, we will write an equivalent ratio with 1 pound of pasta. To find the cost per pound, we can divide both the cost and the weight by 8: \[ \text{Cost per pound} = \frac{12}{8} = \frac{3}{2} = 1.5 \] Thus, the equivalent ratio is: \[ \frac{1.5}{1} \] This means that the cost of 1 pound of pasta is \( \$ 1.50 \). ### Step 4: Calculate Total Cost for 21 Pounds c. Now, to find the total cost for 21 pounds of pasta, we can multiply the cost per pound by the total weight: \[ \text{Total Cost} = \text{Cost per pound} \times \text{Total Weight} = 1.5 \times 21 \] Now, let's calculate this: \[ 1.5 \times 21 = 31.5 \] ### Final Answer The caterer will pay \( \$ 31.50 \) for 21 pounds of pasta. ### Summary of Reasoning - We established the cost per pound to simplify the calculation for any amount of pasta. - By calculating the total cost based on the cost per pound, we arrived at the final answer efficiently.