Question

23 travelers forest 63 piles of plantains containing the same number of plantains and a remaining pile containing 7 plantains. They divided the plantains equally. What is the least number of plantains that each traveler got?

Answer 1

14 plantains

Explanation:

Given

`x \to` plantain in a pile

`y \to` plantain received by each

`n = 23` travelers

Required

The least value of y

Note that:

- There are x plantains in 1 pile, so there will be 63x in 63 piles

- The number of plantains shared is: 7 to 63x (7 represents the single plantain)

- 1 traveler gets y plantains, so 23y will receive 7 + 63x plantains

So, the equation is:

`23y = 7 + 63x`

Make y the subject

`y = (7 + 63x)/(23)`

The values of x and y must be integer and these values must be greater than 0.

Using trial by error method, we test the values of x starting from 1;

So, we have:

`x = 1 \to y = (7 + 63 * 1)/(23) = (70)/(23) = 3.04`

`x = 2 \to y = (7 + 63 * 2)/(23) = (133)/(23) = 5.78`

`x = 3 \to y = (7 + 63 * 3)/(23) = (133)/(23) = 8.52`

`x = 4 \to y = (7 + 63 * 4)/(23) = (259)/(23) = 11.26`

`x = 5 \to y = (7 + 63 * 5)/(23) = (322)/(23) = 14`

So, the smallest values of x and y that satisfy the equation is:

`(x,y)=(5,14)`

Hence, the least number of plantain each traveler got is 14