The problem provides a Venn diagram showing the number of learners who liked Fanta, Coke, and Sprite. We are given that 40 learners liked Fanta. We need to find the value of $x$, the total number of learners in the class, the number of learners who did not like Fanta, and the number of learners who liked two types of drinks only.

1. Problem Description

The problem provides a Venn diagram showing the number of learners who liked Fanta, Coke, and Sprite. We are given that 40 learners liked Fanta. We need to find the value of $x$, the total number of learners in the class, the number of learners who did not like Fanta, and the number of learners who liked two types of drinks only.

2. Solution Steps

i. Find the value of $x$ if 40 learners liked Fanta.

The number of learners who liked Fanta is the sum of the numbers in the Fanta circle: $17 + (x+2) + x + x = 40$.

Simplifying the equation:

$3x + 19 = 40$

$3x = 40 - 19$

$3x = 21$

$x = 21/3$

$x = 7$

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

We need to sum all the numbers in the Venn diagram:

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

Substitute $x = 7$:

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

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

Thus, the total number of learners is

5

3.

iii. a. Find the number of learners who did not like Fanta.

The number of learners who did not like Fanta is the sum of the numbers that are not in the Fanta circle:

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

iii. b. Find the number of learners who liked two types of drinks only.

The number of learners who liked two types of drinks only is the sum of the intersections of two circles, excluding the intersection of all three circles.

Those who liked Fanta and Coke only: $x + 2 = 7 + 2 = 9$

Those who liked Fanta and Sprite only: $x = 7$

Those who liked Coke and Sprite only: $x - 2 = 7 - 2 = 5$

So the total number of learners who liked two types of drinks only is $9 + 7 + 5 = 21$.

3. Final Answer

i. $x = 7$

ii. 53

iii. a. 13

iii. b. 21