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Question
The ratio of fruit trees and vegetable trees in an orchard is 3:4. If 6 more trees of each type are planted, the ratio of trees would be 6:7. Find the number of fruit trees and vegetable trees in the orchard.
The ratio of fruit trees and vegetable trees = 3:4
So, let the number of fruit trees= 3x and the number of vegetable trees = `square`
From the given condition,
`(3x + square)/(square + square) = square/square`
`square (3x + square) = square (square + square)`
`square + square = square + square`
`square - square = square - square`
`- square = - square`
`square = square`
x = `square`
∴ Number of fruit trees in the orchard = 3x = 3 × `square` = `square` and number of vegetable trees in the orchard = 4x = 4 × `square` = `square`
Hence, the number of fruit trees and vegetable trees in the orchard are `square` and `square` respectively.
Solution
The ratio of fruit trees and vegetable trees = 3:4
So, let the number of fruit trees = 3x and the number of vegetable trees = 4x
From the given condition,
`(3x + bb6)/(bb(4x) + bb6) = bb6/bb7`
7(3x + 6) = 6 (4x + 6)
21x + 42 = 24x + 36
21x – 24x = 36 – 42
– 3x = – 6
3x = 6
x = 2
∴ Number of fruit trees in the orchard = 3x = 3 × 2 = 6 and number of vegetable trees in the orchard = 4x = 4 × 2 = 8
Hence, the number of fruit trees and vegetable trees in the orchard are 6 and 8 respectively.
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