Basil, Oscar and Sue share 43 sweets.
Sue gets the largest share.
What is the smallest possible number of sweets Sue could get?

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

Which means

or

(2)

We also said that Basil has the 2nd largest share, so

So we can write:

This means that the minimum share for Basil is 14, and so the minimum share for Sue is