Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. Sheila's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for Sheila to have 15 acres of tangerine trees and 10 acres of grapefruit trees?

Question

07-06-2018
Mathematics

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Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. Sheila's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for Sheila to have 15 acres of tangerine trees and 10 acres of grapefruit trees?

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Matheng Matheng · Answer 1 · 2018-06-17T18:54:25+02:00

Tangerine trees yield 50 pounds of fruit per acre.

Grapefruit trees yield 75 pounds of fruit per acre.

Let the number of acres of tangerine = x

And the number of acres of grapefruit = y
The total produced of fruit = 1,500

The equation which represents the total fruits of tangerine and grapefruit is:

50 x + 75 y = 1500 →→(1)

Now, to answer the given question, Is it possible for Sheila to have 15 acres of tangerine trees and 10 acres of grapefruit trees?
∴ x = 15 and y = 10
By substitution in (1) with x and y
∴ 50 * 15 + 75 * 10 = 750 + 750 = 1500
Which is agree with the total produced from Sheila's orchard.

So, the answer is :
Yes, it is possible for Sheila to have 15 acres of tangerine trees and 10 acres of grapefruit trees.