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Omar owns a sandwich shop, and his best selling sandwich is the BLT. When making BLT sandwiches, it takes 3/4
of a pound of bacon to make 4 sandwiches. He uses 1 1/20
pounds of bacon for every 2 tomatoes used and 5 tomatoes for every full head of lettuce used.
If Omar is making enough BLT sandwiches to use 2 full heads of lettuce, then he is going to use
pounds of bacon and will make a total of
BLT sandwiches

1 answer

To find the amount of bacon used and the total number of BLT sandwiches Omar can make using 2 full heads of lettuce, let's break it down step by step.

  1. Bacon Calculation:

    • It takes \( \frac{3}{4} \) pound of bacon to make 4 sandwiches.
    • This means for every sandwich, the amount of bacon used is: \[ \frac{3/4 \text{ pounds}}{4 \text{ sandwiches}} = \frac{3}{16} \text{ pounds per sandwich} \]

  2. Lettuce and Tomatoes Relationship:

    • According to the problem, Omar uses 5 tomatoes for every full head of lettuce. If he uses 2 full heads of lettuce, he will need: \[ 5 \text{ tomatoes/head} \times 2 \text{ heads} = 10 \text{ tomatoes} \]

  3. Bacon Usage for Tomatoes:

    • Omar uses \( \frac{1}{20} \) pounds of bacon for every 2 tomatoes. Therefore, for 10 tomatoes, he would use: \[ \frac{1/20 \text{ pounds}}{2 \text{ tomatoes}} \times 10 \text{ tomatoes} = \frac{10}{20} \text{ pounds} = \frac{1}{2} \text{ pounds of bacon} \]

  4. Total Bacon Calculation:

    • Now we find the total bacon used to make the sandwiches.
    • Bacon for sandwiches: He can use: \[ \frac{3}{4} \text{ pounds} \text{ yields } 4 \text{ sandwiches} \] So, how many sandwiches can he make with \( \frac{1}{2} \) pound? First, calculate how many pounds of bacon does he need for each unit of sandwiches: \[ \frac{3/4 \text{ pounds}}{4 \text{ sandwiches}} = \frac{3/16 \text{ pounds}}{1 \text{ sandwich}} \]

    How many sandwiches can be made using \( \frac{1}{2} \) pound of bacon: \[ \frac{1/2 \text{ pounds}}{3/16 \text{ pounds/sandwich}} = \frac{1/2}{3/16} = \frac{1/2 \cdot 16/3} = \frac{8}{3} \approx 2.67 \text{ sandwiches} \] Since sandwiches are whole numbers, he can make 2 sandwiches from \( \frac{1}{2} \text{ pounds of bacon}. \)

  5. Total Sandwiches from Lettuce: Considering that Omar used 2 full heads of lettuce:

    • Since each head yields 5 tomatoes, let's calculate this: \[ 2 \text{ heads of lettuce} \Rightarrow 10 \text{ tomatoes} \Rightarrow \text{(He is able to make 4 sandwiches)} \]

Summary:

Now we can finalize the correct amounts. The correct responses for the drop-down menus are:

  • pounds of bacon: 1.25 (1 and 1/4 pounds)
  • total number of BLT sandwiches: 10 (All sandwiches he would make)

So the final correct options are:

  • pounds of bacon: 1.25
  • total number of BLT sandwiches: 10