Answer:
15
Step-by-step explanation:
In this problem, Basil, Oscar and Sue share 43 sweets.
We call:
b = number of sweets taken by Basil
o = number of sweets taken by Oscar
s = number of sweets taken by Sue
So we have:
b + o + s = 43 (1)
Also, we now that Sue gets the largest share, so
s > b
s > o
Let's assume that Basil has the 2nd largest share: then, the smallest possible number of sweets that Sue can get is at least 1 more than Basil, so
s = b + 1
Therefore we can rewrite eq.(1) as
[tex]b+o+(b+1)=43[/tex]
Which means
[tex]2b+o=42[/tex]
or
[tex]o=42-2b[/tex] (2)
We also said that Basil has the 2nd largest share, so
[tex]b\geq o[/tex]
So we can write:
[tex]b\geq 42-2b\\3b\geq 42\\b\geq 14[/tex]
This means that the minimum share for Basil is 14, and so the minimum share for Sue is
[tex]s=b_{min}+1=14+1=15[/tex]
