Question

A chef is preparing a major dinner event and needs bell peppers, onions, and tomatoes in mass quantity from the produce outlet she utilizes. The bell peppers are sold in quantities of 3, the onions are sold in quantities of 6, and the tomatoes are sold in quantities of 7. Given the packaging, what is the smallest number of each the chef can order to ensure that she has exactly the same amount of each (not the number of packages, but rather the number of each type of produce)?

Answer 1

The smallest number of each type of vegetable the chef can order to have an equal amount is 42. The Least Common Multiple (LCM) of 3, 6, and 7 is 42, therefore 14 packs of bell peppers, 7 packs of onions, and 6 packs of tomatoes will all yield 42 vegetables each.

Step-by-step explanation:

The student is seeking to find the smallest number of bell peppers, onions, and tomatoes that can be ordered so that the chef has an equal number of each type of vegetable. This problem can be solved using the concept of least common multiple (LCM). Bell peppers come in packs of 3, onions in packs of 6, and tomatoes in packs of 7. The smallest number that is a multiple of 3, 6, and 7 is the LCM of these numbers.

First, we list a few multiples of each:

• Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27,...
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42,...
• Multiples of 7: 7, 14, 21, 28, 35, 42, 49,...

From these lists, we find that 42 is the smallest multiple common to all three sets. Therefore, the chef can order 14 packs of bell peppers (3 x 14 = 42), 7 packs of onions (6 x 7 = 42), and 6 packs of tomatoes (7 x 6 = 42) to have exactly 42 of each type of vegetable.