The problem presents a Venn diagram showing the number of learners who like 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 presents a Venn diagram showing the number of learners who like 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 $x$:

The number of learners who liked Fanta is the sum of the regions within the Fanta circle.

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

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

$2x + 26 = 40$

$2x = 40 - 26$

$2x = 14$

$x = 7$

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

We need to sum all the numbers in the Venn diagram. First, we substitute $x = 7$ into the Venn diagram regions.

$x+2 = 7+2 = 9$

$x-2 = 7-2 = 5$

The numbers in the Venn diagram are $17, 9, 5, 7, 7, 5, 3$.

Total number of learners $= 17 + 9 + 5 + 7 + 7 + 5 + 3 = 53$

iii.

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

This is the sum of the regions outside the Fanta circle. These are the learners who only like Coke, only like Sprite, and those who like Coke and Sprite but not Fanta. Thus $5 + 5 + 3 = 13$.

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

These are the learners in the regions where two circles intersect, but not all three.

Fanta and Coke only: $x+2 = 9$

Fanta and Sprite only: $x = 7$

Coke and Sprite only: $x-2 = 5$

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

3. Final Answer

i. $x = 7$

ii. The total number of learners in the class is

5

3. iii.

a. The number of learners who did not like Fanta is

1

3. b. The number of learners who liked two types of drinks only is 21.