Final answer:
The cooks can make 69 hamburgers with 46 2/3 pounds of beef. If they have twice as much beef, they can make 138 hamburgers. If they have half as much beef, they can make 34 hamburgers.
Step-by-step explanation:
To find out how many hamburgers the cooks can make with 46 2/3 pounds of beef, we need to divide the total weight of beef by the weight used per hamburger.
First, let's convert the mixed number 46 2/3 to an improper fraction. Multiply the whole number by the denominator and add the numerator. So, 46 2/3 becomes (46x3 + 2)/3 = 138/3.
Next, we divide 138/3 by 2/3 to find the number of hamburgers. When we divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. So, (138/3) ÷ (2/3) = (138/3) × (3/2) = 138/2 = 69.
Therefore, the cooks can make 69 hamburgers with 46 2/3 pounds of beef.
If the cooks have twice as much beef, they would have 46 2/3 × 2 = 93 1/3 pounds of beef. Following the same steps as above, they would be able to make 69 × 2 = 138 hamburgers.
If the cooks have half as much beef, they would have 46 2/3 ÷ 2 = 23 1/3 pounds of beef. Using the same steps as before, they would be able to make 69 ÷ 2 = 34.5 hamburgers. Since we cannot have a fraction of a hamburger, they would be able to make 34 hamburgers.