Answer:
14 plantains
Step-by-step explanation:
Given
[tex]x \to[/tex] plantain in a pile
[tex]y \to[/tex] plantain received by each
[tex]n = 23[/tex] 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:
[tex]23y = 7 + 63x[/tex]
Make y the subject
[tex]y = \frac{7 + 63x}{23}[/tex]
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:
[tex]x = 1 \to y = \frac{7 + 63 * 1}{23} = \frac{70}{23} = 3.04[/tex]
[tex]x = 2 \to y = \frac{7 + 63 * 2}{23} = \frac{133}{23} = 5.78[/tex]
[tex]x = 3 \to y = \frac{7 + 63 * 3}{23} = \frac{133}{23} = 8.52[/tex]
[tex]x = 4 \to y = \frac{7 + 63 * 4}{23} = \frac{259}{23} = 11.26[/tex]
[tex]x = 5 \to y = \frac{7 + 63 * 5}{23} = \frac{322}{23} = 14[/tex]
So, the smallest values of x and y that satisfy the equation is:
[tex](x,y)=(5,14)[/tex]
Hence, the least number of plantain each traveler got is 14
