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Sagot :
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:
[tex]40+\frac{45}{2}=\frac{40\times2+1\times45}{1\times2}=\frac{80+45}{2}=\frac{125}{2}[/tex]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:
[tex]\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}[/tex]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:
[tex]4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{12+1}{3}=\frac{13}{3}[/tex]Now, apply proportions:
[tex]\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}[/tex]You also can convert this fraction into a mixed number:
[tex]\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}[/tex]Then, they'll need to order 10 5/6 pounds of deli meats for the party.
c. Lasagna
Convert the mixed number to fraction:
[tex]10\frac{3}{4}=\frac{10\times4+3}{4}=\frac{40+3}{4}=\frac{43}{4}[/tex]Apply proportions:
[tex]\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}[/tex]You also can convert this fraction into a mixed number:
[tex]\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}[/tex]Then, they'll need to order 26 7/8 pounds of lasagna for the party.
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