Question

2.6 ps-9
count each of these \drop - in\ guests as half a guest. how much of each food item should sydney and nathan order for a graduation party with 45 drop - in guests?
sydney and nathan should order
square pounds of lasagna.
(the table shows: chicken: pieces, deli meats: 2/3 pounds, lasagna: 1 3/4 pounds?)
enter your answer in the answer box and then click check answer.

Explanation:

Step1: Identify the amount per guest

Each "drop - in" guest is considered as half a guest. So the number of equivalent full guests for lasagna is calculated by multiplying the number of drop - in guests (45) by 0.5. Let's denote the amount of lasagna per full guest as $1\frac{3}{4}$ pounds (which is $\frac{1\times4 + 3}{4}=\frac{7}{4}$ pounds).

Step2: Calculate the total amount of lasagna

First, find the number of equivalent full guests: $45\times0.5 = 22.5=\frac{45}{2}$. Then, multiply this by the amount per full guest. The amount per full guest is $\frac{7}{4}$ pounds. So the total amount $T=\frac{45}{2}\times\frac{7}{4}=\frac{315}{8}=39\frac{3}{8}$? Wait, no, wait. Wait, maybe I misread. Wait, the table: Lasagna is $1\frac{3}{4}$ pounds per guest? Wait, no, the problem says "count each of these 'drop - in' guests as half a guest". Wait, maybe the lasagna amount per guest (full guest) is $1\frac{3}{4}$ pounds. So for 45 drop - in guests, each is 0.5 guest, so total guest equivalents: $45\times0.5 = 22.5$. Then total lasagna: $22.5\times1\frac{3}{4}$. Convert $1\frac{3}{4}$ to decimal: $1.75$, $22.5\times1.75 = 39.375=\frac{315}{8}=39\frac{3}{8}$? Wait, no, maybe the lasagna per guest (drop - in) is half of $1\frac{3}{4}$? Wait, no, the problem says "count each of these 'drop - in' guests as half a guest". So if a full guest gets $1\frac{3}{4}$ pounds, a drop - in guest (half guest) gets half of that? Wait, no, the wording is "count each of these 'drop - in' guests as half a guest". So when calculating the total, we can treat the 45 drop - in guests as $45\times0.5 = 22.5$ full guests. Then, if the amount per full guest is $1\frac{3}{4}$ pounds, then total lasagna is $22.5\times1\frac{3}{4}$. Let's do it as fractions. $22.5=\frac{45}{2}$, $1\frac{3}{4}=\frac{7}{4}$. So $\frac{45}{2}\times\frac{7}{4}=\frac{315}{8}=39\frac{3}{8}$? Wait, but maybe the lasagna per drop - in guest is $1\frac{3}{4}\div2$? Wait, no, the problem says "count each of these 'drop - in' guests as half a guest". So the total number of guests (in terms of full guests) is $45\times0.5 = 22.5$. Then, if the amount per full guest is $1\frac{3}{4}$ pounds, then total is $22.5\times1\frac{3}{4}$. Let's calculate $1\frac{3}{4}=\frac{7}{4}$, $22.5=\frac{45}{2}$. $\frac{45}{2}\times\frac{7}{4}=\frac{315}{8}=39.375 = 39\frac{3}{8}$? Wait, but maybe I misread the table. Wait, the table has Lasagna as $1\frac{3}{4}$ pounds per guest? Wait, the original problem: "count each of these 'drop - in' guests as half a guest. How much of each food item should Sydney and Nathan order for a graduation party with 45 drop - in guests?" And the table: Lasagna is $1\frac{3}{4}$ pounds per guest (full guest). So for 45 drop - in guests, each is 0.5 guest, so total guest units: $45\times0.5 = 22.5$. Then total lasagna: $22.5\times1\frac{3}{4}$. Let's compute $1\frac{3}{4}=1.75$, $22.5\times1.75 = 39.375=\frac{315}{8}=39\frac{3}{8}$? Wait, no, maybe the lasagna per drop - in guest is $1\frac{3}{4}\times0.5$? Wait, no, the "count as half a guest" means that the number of guests is halved. So instead of 45 guests, we have 45/2 guests. Then, amount per guest (full) is $1\frac{3}{4}$, so total is (45/2)×(7/4)=315/8 = 39.375 = 39 3/8. Wait, but maybe I made a mistake. Wait, let's re - read. The problem says "count each of these 'drop - in' guests as half a guest". So for example, if a full guest needs x pounds, a drop - in guest needs x/2 pounds. But maybe the table says lasagna is $1\frac{3}{4}$ pounds per full guest. So for 45 drop - in guests, total lasagna is 45×(1\frac{3}{4}×0.5). Let's compute that. 1\frac{3}{4}×0.5=\frac{7}{4}×\frac{1}{2}=\frac{7}{8}$. Then 45×\frac{7}{8}=\frac{315}{8}=39\frac{3}{8}$. Yes, that's correct. So the total amount of lasagna is $\frac{315}{8}=39\frac{3}{8}$ pounds. Wait, but let's check the calculation again. 45 drop - in guests, each is half a guest. So the number of "full guest equivalents" is 45×0.5 = 22.5. The amount per full guest is $1\frac{3}{4}=\frac{7}{4}$. So 22.5×\frac{7}{4}. 22.5 is $\frac{45}{2}$, so $\frac{45}{2}×\frac{7}{4}=\frac{315}{8}=39.375 = 39\frac{3}{8}$. So the total pounds of lasagna is $39\frac{3}{8}$.

Answer:

$39\frac{3}{8}$