Let's break down the problem step by step to find the values requested:
-
Determine the amount of bacon used per head of lettuce:
-
Omar uses 5 tomatoes for every full head of lettuce.
-
He needs 1 1/20 pounds of bacon for every 2 tomatoes used, which can be converted to an improper fraction: \[ 1 \frac{1}{20} = \frac{21}{20} \text{ pounds of bacon per 2 tomatoes} \]
-
Since there are 5 tomatoes per head of lettuce, we can calculate the amount of bacon needed for 5 tomatoes: \[ \text{Tomatoes per head of lettuce} = 5 \]
- The number of pairs of tomatoes (since the bacon is measured per 2 tomatoes) is \( \frac{5}{2} = 2.5 \) pairs.
-
Hence, the amount of bacon needed for 5 tomatoes is: \[ \frac{21}{20} \times 2.5 = \frac{21}{20} \times \frac{5}{2} = \frac{21 \times 5}{20 \times 2} = \frac{105}{40} = \frac{21}{8} \text{ pounds of bacon for 1 head of lettuce} \]
-
-
Calculate bacon used for 2 heads of lettuce:
- If he uses 2 full heads of lettuce, the total amount of bacon needed is: \[ \frac{21}{8} \times 2 = \frac{42}{8} = \frac{21}{4} \text{ pounds of bacon} \]
-
Determine the number of sandwiches made per 3/4 lb of bacon:
-
From the problem, we know that it takes 3/4 pounds of bacon to make 4 sandwiches.
-
Therefore, he can calculate how many sandwiches he can make with \( \frac{21}{4} \) pounds of bacon:
- First, find out how many 3/4 lb portions are in \( \frac{21}{4} \): \[ \text{Number of portions} = \frac{\frac{21}{4}}{\frac{3}{4}} = \frac{21}{4} \times \frac{4}{3} = \frac{21}{3} = 7 \]
-
Since each portion produces 4 sandwiches: \[ \text{Total sandwiches} = 7 \times 4 = 28 \text{ sandwiches} \]
-
So, the final answer is as follows:
- Omar is going to use \( \frac{21}{4} \) pounds of bacon and will make a total of 28 BLT sandwiches.
To summarize:
- Pounds of bacon: \( \frac{21}{4} \)
- Total BLT sandwiches: 28