The problem presents a Venn diagram showing the number of learners who liked Fanta, Coke, and Sprite. We are given that 40 learners liked Fanta and are asked to find the value of $x$. Then, we need to find the total number of learners in the class and the number of learners who did not like Fanta.

1. Problem Description

The problem presents a Venn diagram showing the number of learners who liked Fanta, Coke, and Sprite. We are given that 40 learners liked Fanta and are asked to find the value of $x$. Then, we need to find the total number of learners in the class and the number of learners who did not like Fanta.

2. Solution Steps

i. Find the value of $x$.

The number of learners who liked Fanta is the sum of the regions within the Fanta circle: $17 + (x+2) + x + 7$. We are given that this sum equals

4

0. $17 + (x+2) + x + 7 = 40$

$17 + x + 2 + x + 7 = 40$

$2x + 26 = 40$

$2x = 40 - 26$

$2x = 14$

$x = \frac{14}{2}$

$x = 7$

ii. Find the total number of learners in the class.

We need to sum all the numbers in the Venn diagram: $17 + (x+2) + 5 + x + (x-2) + 7 + 3$. Substituting $x=7$:

$17 + (7+2) + 5 + 7 + (7-2) + 7 + 3$

$17 + 9 + 5 + 7 + 5 + 7 + 3 = 53$

So the total number of learners is

5

3.

iii. How many learners did not like Fanta?

The learners who did not like Fanta are those in the Coke only region, the Sprite only region, and the region where the Coke and Sprite circles intersect but not Fanta. This is $5 + (x-2) + 3$. Substituting $x = 7$:

$5 + (7-2) + 3 = 5 + 5 + 3 = 13$

3. Final Answer

i. $x = 7$

ii. Total number of learners in the class: $53$

iii. Number of learners who did not like Fanta: $13$