Question

The table lists recommended amounts of food to order for 25 party guests. Amanda and Syndey are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should Amanda and Syndey order for a graduation party with 45 drop-in guests?

Answer 1

Amanda and Sydney are hosting a graduation party for 40 guests.

Also, they have 45 drop-in guests (each of these will count as half a guest).

Then, the total number of guests is:

$40+\frac{45}{2}=\frac{40\times2+1\times45}{1\times2}=\frac{80+45}{2}=\frac{125}{2}$

The table shows the recommended amounts of food for 25 party guests:

Fried Chicken: 24 pieces

Deli meats: 4 1/3 pounds

Lasagna: 10 3/4 pounds.

Let's find the proportion for 125/2 guests:

a. Fried chicken:

$\begin{gathered} \frac{24\text{ pieces}}{25\text{ guests}}=\frac{x\text{ pieces}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ 24\times\frac{125}{2}=x\times25 \\ \frac{24\times125}{2}=x\times25 \\ 1500=x\times25 \\ \text{Divide both sides by 25} \\ \frac{1500}{25}=\frac{x\times25}{25} \\ \text{Simplify} \\ 60=x \end{gathered}$

Then, they'll need to order 60 units of fried chicken for the party.

b. Deli meats:

Start by converting the mixed number 4 1/3 into a fraction:

$4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{12+1}{3}=\frac{13}{3}$

Now, apply proportions:

$\begin{gathered} \frac{13/3\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{13}{3}\times\frac{125}{2} \\ x\times25=\frac{13\times125}{3\times2} \\ x\times25=\frac{1625}{6} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{1625}{6\times25}=\frac{1625}{150}=\frac{65}{6} \\ \text{Simplify} \\ x=\frac{65}{6} \end{gathered}$

You also can convert this fraction into a mixed number:

$\begin{gathered} \text{When you divide 65/6 you obtain a quotient of 10 and remainder 5.} \\ \text{Then the whole part is 10 and the fraction is 5/6} \\ \frac{65}{6}=10\frac{5}{6} \end{gathered}$

Then, they'll need to order 10 5/6 pounds of deli meats for the party.

c. Lasagna

Convert the mixed number to fraction:

$10\frac{3}{4}=\frac{10\times4+3}{4}=\frac{40+3}{4}=\frac{43}{4}$

Apply proportions:

$\begin{gathered} \frac{43/4\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{43}{4}\times\frac{125}{2} \\ x\times25=\frac{43\times125}{4\times2} \\ x\times25=\frac{5375}{8} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{5375}{8\times25}=\frac{5375}{200}=\frac{215}{8} \\ \text{Simplify} \\ x=\frac{215}{8} \end{gathered}$

You also can convert this fraction into a mixed number:

$\begin{gathered} \text{When you divide 215/8 you obtain a quotient of 26 and remainder 7.} \\ \text{Then the whole part is 26 and the fraction is 7/}8 \\ \frac{215}{8}=26\frac{7}{8} \end{gathered}$

Then, they'll need to order 26 7/8 pounds of lasagna for the party.