Given :- Grandfather wants to GIVE his 441 olive trees to his 18 sons and GRANDSONS so that every son gets 5 trees more than every grandson. How many trees every son should get ?

Answer :-

Let us assume that, total sons in the family are x and each grandson gets y number of olive trees .

so, we have,

son grandson

x (18 - x)

(y + 5) y

then,

→ Total olive trees = 441

→ x(y + 5) + y(18 - x) = 441

→ xy + 5x + 18y - xy = 441

→ 5x + 18y = 441

→ 18y = (441 - 5x)

→ y = (441 - 5x)/18

conclusion :-

• x is number of sons , that must be a natural number .
• x = odd number , since it has to be DIVISIBLE by 18 . As multiple of 18 are even numbers only . (odd - odd = even)

putting VALUES of x = odd natural numbers we get, since y must be a natural number also .

then,

• x = 1 => (441 - 5)/18 ≠ Natural number .
• x = 3 => (441 - 15)/18 ≠ Natural number .
• x = 5 => (441 - 25)/18 ≠ Natural number .
• x = 7 => (441 - 35)/18 ≠ Natural number .
• x = 9 => (441 - 45)/18 = 396/18 = 22 = Natural number .

hence,

→ Number of olive trees every son should gets = (y + 5) = 22 + 5 = 27 trees (Ans.)

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