Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. John's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for John to have 25 acres of tangerine trees and 15 acres of grapefruit trees?

No, because 50 (25) + 75 (15) ≠ 1500 No, because (50 + 75) (20 + 15) ≠ 1500 Yes, because 50 (25) + 75 (15) ≥ 1500 Yes, because 50 + 75 + 25 + 15 ≤ 1500

Question

Mathematics

Snuffles

6 April, 05:43

Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. John's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for John to have 25 acres of tangerine trees and 15 acres of grapefruit trees?

No, because 50 (25) + 75 (15) ≠ 1500 No, because (50 + 75) (20 + 15) ≠ 1500 Yes, because 50 (25) + 75 (15) ≥ 1500 Yes, because 50 + 75 + 25 + 15 ≤ 1500

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Answers (1)

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Alma Mckee · Answer 1

If x and y are the acres under Tangerine trees and grapefruit trees respectively, then:

Total pounds of trees = 50x + 75y

For x = 25 acres and y = 15 acres

Total weight of trees = 50*25 + 75*15 = 2,375 pounds

This exceeds the maximum weight of fruits (that is, 1,500 pounds) possible from this farm. Therefore, John cannot have 25 acres of Tangerine trees and 15 acres of grapefruit trees.