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.

Answer 1

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.