Question 2. (ALL CALCULATIONS MUST BE DONE WITHOUT USING A CALCULATOR) 2.1.1 Increase R68 in the ratio $$ 7: 4 $$ 2.1.2 Decrease $$ 91 x $$ in the ratio $$ 5: 7 $$. 2.1.3 Divide 182 kg in the ratio $$ 2: 3: 8 $$. 2.2 A farmer can exchange 72 pigs for 54 sheep at R560 each. What is the price of a pig 2.3 The ratio of the number of boys to the number of girls in a class is $$ 4: 3 $$. 2.3.1 Calculate how many boys there are in the class if there are 42 pupils in the class. 2.3.2 Calculate how many pupils there are in the class if there are 21 girls. Question 3

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### 2.1.1 Increase R68 in the ratio $$ 7: 4 $$

To increase R68 in the ratio $$ 7: 4 $$, we first need to find the total parts of the ratio:

$$
\text{Total parts} = 7 + 4 = 11
$$

Now, we can find the value of one part:

$$
\text{Value of one part} = \frac{68}{4} = 17
$$

Now, we can calculate the increased amount:

$$
\text{Increased amount} = 7 \times 17 = 119
$$

So, R68 increased in the ratio $$ 7: 4 $$ is R119.

### 2.1.2 Decrease $$ 91x $$ in the ratio $$ 5: 7 $$

To decrease $$ 91x $$ in the ratio $$ 5: 7 $$, we first find the total parts of the ratio:

$$
\text{Total parts} = 5 + 7 = 12
$$

Now, we can find the value of one part:

$$
\text{Value of one part} = \frac{91x}{7} = \frac{91}{7}x
$$

Now, we can calculate the decreased amount:

$$
\text{Decreased amount} = 5 \times \frac{91}{7}x = \frac{455}{7}x
$$

So, $$ 91x $$ decreased in the ratio $$ 5: 7 $$ is $$ \frac{455}{7}x $$.

### 2.1.3 Divide 182 kg in the ratio $$ 2: 3: 8 $$

To divide 182 kg in the ratio $$ 2: 3: 8 $$, we first find the total parts of the ratio:

$$
\text{Total parts} = 2 + 3 + 8 = 13
$$

Now, we can find the value of one part:

$$
\text{Value of one part} = \frac{182}{13} = 14
$$

Now, we can calculate each part:

- For the first part (2 parts):
$$
\text{First part} = 2 \times 14 = 28 \text{ kg}
$$

- For the second part (3 parts):
$$
\text{Second part} = 3 \times 14 = 42 \text{ kg}
$$

- For the third part (8 parts):
$$
\text{Third part} = 8 \times 14 = 112 \text{ kg}
$$

So, 182 kg divided in the ratio $$ 2: 3: 8 $$ is 28 kg, 42 kg, and 112 kg.

### 2.2 A farmer can exchange 72 pigs for 54 sheep at R560 each. What is the price of a pig?

First, we find the total value of the sheep:

$$
\text{Total value of sheep} = 54 \times 560 = 30240
$$

Now, we can find the price of one pig:

$$
\text{Price of one pig} = \frac{30240}{72} = 420
$$

So, the price of a pig is R420.

### 2.3 The ratio of the number of boys to the number of girls in a class is $$ 4: 3 $$.

#### 2.3.1 Calculate how many boys there are in the class if there are 42 pupils in the class.

The total parts of the ratio $$ 4: 3 $$ is:

$$
\text{Total parts} = 4 + 3 = 7
$$

Now, we can find the value of one part:

$$
\text{Value of one part} = \frac{42}{7} = 6
$$

Now, we can calculate the number of boys:

$$
\text{Number of boys} = 4 \times 6 = 24
$$

So, there are 24 boys in the class.

#### 2.3.2 Calculate how many pupils there are in the class if there are 21 girls.

If there are 21 girls, we can find the value of one part:

$$
\text{Value of one part} = \frac{21}{3} = 7
$$

Now, we can calculate the total number of pupils:

$$
\text{Total pupils} = 7 \times 7 = 49
$$

So, there are 49 pupils in the class.

### Summary of Answers:
- 2.1.1: R119
- 2.1.2: $$ \frac{455}{7}x $$
- 2.1.3: 28 kg, 42 kg, 112 kg
- 2.2: R420
- 2.3.1: 24 boys
- 2.3.2: 49 pupils
- 2.1.1: R119 - 2.1.2: $$ \frac{455}{7}x $$ - 2.1.3: 28 kg, 42 kg, 112 kg - 2.2: R420 - 2.3.1: 24 boys - 2.3.2: 49 pupils

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