A caterer has determined that the amount of meat to order for a particular entrée varies proportionally to the number of guests. If there are 25 guests, the caterer needs to order 40 pounds of meat. How much meat should the caterer order if there are 100 guests??

Answer 1

To determine how much meat the caterer should order based on the number of guests, we can use the concept of direct proportionality.

Given that the amount of meat needed (M) is proportional to the number of guests (N), we can express this relationship as:

\[ M = k \cdot N \]

where \(k\) is the constant of proportionality.

From the information provided, when there are 25 guests, the caterer orders 40 pounds of meat:

\[ 40 = k \cdot 25 \]

To find \(k\), we can solve for it:

\[ k = \frac{40}{25} = \frac{8}{5} = 1.6 \]

Now that we have determined \(k\), we can calculate the amount of meat needed for 100 guests:

\[ M = k \cdot N = 1.6 \cdot 100 \]

Calculating this gives:

\[ M = 160 \]

Thus, the caterer should order 160 pounds of meat for 100 guests.