Answer to the Patterns Question

Question:

The average apple tree produces between 200 and 400 apples per year. If a farmer has 30 trees:

• What is the minimum number of apples the trees will produce?
• What is the maximum number of apples the trees will produce?
• If 1/3 of the trees produce the minimum number of apples, 2/5 of the trees produce an average number of apples, and the remaining trees produce the maximum number of apples, how many apples will the farmer have?

Answer:

• minimum = 200 per tree
  30 x 200 = 6 000 apples
• maximum = 400 per tree
  30 x 400 = 12 000 apples
• minimum → 1/3 of 30 = 10 x 200 = 2000 apples
  average →2/5 of 30 = 12
  average apples = (200 + 400) ÷ 2 = 300
  12 x 300 = 3 600
  Maximum →30 – 10 – 12 = 8
  8 x 400 = 3 600
  Total number of apples = 2 000 + 3 600 + 3 600
  = 9 200