3.6 Increase 99 in the ratio $$ 12: 11 $$ $$ \qquad $$ $$ \qquad $$ (2 [1 QUESTION 4 4.1 The price of an item in United states of America was US\$230 on a particular day. The exchange rate on this day was US\$1 : R17,80. Calculate the cost of this item in Rand value. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (2 4.2 Determine $$ 15 \% $$ of 300 kg . $$ \qquad $$ $$ \qquad $$ (1 4.3 The cost of a loaf of bread in a shop was R11,50. This price was increased by $$ 6 \% $$. Calculate the new price of the same loaf of bread in this shop. $$ \qquad $$ $$ \qquad $$ (2 4.4 A shop sells cool drinks at R24 each, including $$ 14 \% $$ VAT. What is the price of a cool drink, excluding VAT?

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Let's solve each part of the problem step by step.

### Question 3.6
**Increase 99 in the ratio $$ 12: 11 $$**

To increase 99 in the ratio $$ 12: 11 $$, we first need to find the amount to increase.

1. **Calculate the total parts in the ratio:**
   $$
   \text{Total parts} = 12 + 11 = 23
   $$

2. **Calculate the increase amount:**
   The increase amount can be calculated as follows:
   $$
   \text{Increase} = 99 \times \frac{12}{11}
   $$

Now, let's calculate the increase.

### Question 4.1
**Calculate the cost of an item in Rand value.**

1. **Given:**
   - Price in USD = 230
   - Exchange rate = 1 USD : R17.80

2. **Calculate the cost in Rand:**
   $$
   \text{Cost in Rand} = 230 \times 17.80
   $$

### Question 4.2
**Determine $$ 15\% $$ of 300 kg.**

1. **Calculate $$ 15\% $$ of 300:**
   $$
   15\% \text{ of } 300 = 0.15 \times 300
   $$

### Question 4.3
**Calculate the new price of the loaf of bread after a $$ 6\% $$ increase.**

1. **Given:**
   - Original price = R11.50
   - Increase = $$ 6\% $$

2. **Calculate the new price:**
   $$
   \text{New Price} = 11.50 + (11.50 \times 0.06)
   $$

### Question 4.4
**Calculate the price of a cool drink excluding VAT.**

1. **Given:**
   - Price including VAT = R24
   - VAT = $$ 14\% $$

2. **Calculate the price excluding VAT:**
   $$
   \text{Price excluding VAT} = \frac{24}{1 + 0.14}
   $$

Now, let's perform the calculations for each part.
Calculate the value by following steps:
- step0: Calculate:
  $$0.15\times 300$$
- step1: Multiply the numbers:
  $$45$$
Calculate or simplify the expression $$ 24 / (1 + 0.14) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{24}{\left(1+0.14\right)}$$
- step1: Remove the parentheses:
  $$\frac{24}{1+0.14}$$
- step2: Add the numbers:
  $$\frac{24}{1.14}$$
- step3: Convert the expressions:
  $$\frac{24}{\frac{57}{50}}$$
- step4: Multiply by the reciprocal:
  $$24\times \frac{50}{57}$$
- step5: Reduce the numbers:
  $$8\times \frac{50}{19}$$
- step6: Multiply:
  $$\frac{8\times 50}{19}$$
- step7: Multiply:
  $$\frac{400}{19}$$
Calculate or simplify the expression $$ 230 * 17.80 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$230\times 17.8$$
- step1: Multiply the numbers:
  $$4094$$
Calculate or simplify the expression $$ 99 * (12/11) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$99\times \frac{12}{11}$$
- step1: Reduce the numbers:
  $$9\times 12$$
- step2: Multiply the numbers:
  $$108$$
Calculate or simplify the expression $$ 11.50 + (11.50 * 0.06) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$11.5+\left(11.5\times 0.06\right)$$
- step1: Multiply the numbers:
  $$11.5+0.69$$
- step2: Add the numbers:
  $$12.19$$
Here are the detailed solutions for each part of the problem:

### Question 3.6
**Increase 99 in the ratio $$ 12: 11 $$**

The increase amount is calculated as:
$$
\text{Increase} = 99 \times \frac{12}{11} = 108
$$
Thus, the increase in 99 in the ratio $$ 12: 11 $$ is **108**.

---

### Question 4.1
**Calculate the cost of an item in Rand value.**

The cost in Rand is calculated as:
$$
\text{Cost in Rand} = 230 \times 17.80 = 4094
$$
Thus, the cost of the item in Rand value is **R4094**.

---

### Question 4.2
**Determine $$ 15\% $$ of 300 kg.**

Calculating $$ 15\% $$ of 300:
$$
15\% \text{ of } 300 = 0.15 \times 300 = 45
$$
Thus, $$ 15\% $$ of 300 kg is **45 kg**.

---

### Question 4.3
**Calculate the new price of the loaf of bread after a $$ 6\% $$ increase.**

The new price is calculated as:
$$
\text{New Price} = 11.50 + (11.50 \times 0.06) = 12.19
$$
Thus, the new price of the loaf of bread is **R12.19**.

---

### Question 4.4
**Calculate the price of a cool drink excluding VAT.**

The price excluding VAT is calculated as:
$$
\text{Price excluding VAT} = \frac{24}{1 + 0.14} = \frac{24}{1.14} \approx 21.05
$$
Thus, the price of a cool drink, excluding VAT, is approximately **R21.05**.

---

If you have any further questions or need additional assistance, feel free to ask!
- **Question 3.6:** Increase 99 in the ratio $$ 12:11 $$ is **108**. - **Question 4.1:** The cost of the item in Rand is **R4094**. - **Question 4.2:** $$ 15\% $$ of 300 kg is **45 kg**. - **Question 4.3:** The new price of the loaf of bread is **R12.19**. - **Question 4.4:** The price of a cool drink excluding VAT is approximately **R21.05**.

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