3.4 Susan bak drie brode. Elke brood het sy ele afmetings, en sy kry skaam om dit to te bedien. shean besluit dat sy die brode gaan sny, dat elke stukkie dieselfde lengte het. Die lengtes van die de, brode is as volg: $$ 15 \mathrm{~cm}, 20 \mathrm{~cm} $$ en 30 cm . 3.4.1 Wat sal die lengte van 'n stukkie brood wees, indien elke stukkie nou ewe lank gesny is? 3.4.2 Hoeveel mense kan van die brood eet, indien elkeen slegs een stukkie eet? (2) 3.5 Luhan het R19800 gespaar vir 'n vakansie oorsee. Die wisselkoers is \$1:R15,76. Hoeveel \$he om op die vakansie te spandeer? (2) 3.6 Johan weeg twee keer soveel soos Melissa. Lian weeg 1,5 keer meer as Johan. Hoeveel we Johan in kg , indien hul gewig saam 180 kg is? 28

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### Problem 3.4

#### 3.4.1
We need to find the length of each piece of bread when the three loaves of bread are cut into equal lengths. The lengths of the loaves are $$ 15 \, \text{cm} $$, $$ 20 \, \text{cm} $$, and $$ 30 \, \text{cm} $$.

To find the length of each piece, we need to determine the greatest common divisor (GCD) of these three lengths.

1. **Finding the GCD of $$ 15 $$, $$ 20 $$, and $$ 30 $$**:
   - The factors of $$ 15 $$ are $$ 1, 3, 5, 15 $$.
   - The factors of $$ 20 $$ are $$ 1, 2, 4, 5, 10, 20 $$.
   - The factors of $$ 30 $$ are $$ 1, 2, 3, 5, 6, 10, 15, 30 $$.

The common factors are $$ 1, 5 $$. The greatest common factor is $$ 5 $$.

Thus, the length of each piece of bread will be $$ 5 \, \text{cm} $$.

#### 3.4.2
Next, we need to determine how many pieces of bread can be made from the three loaves if each piece is $$ 5 \, \text{cm} $$ long.

1. **Calculating the total length of the bread**:
   $$
   \text{Total length} = 15 + 20 + 30 = 65 \, \text{cm}
   $$

2. **Calculating the number of pieces**:
   $$
   \text{Number of pieces} = \frac{\text{Total length}}{\text{Length of each piece}} = \frac{65}{5} = 13
   $$

So, $$ 13 $$ people can eat from the bread if each person eats one piece.

### Problem 3.5
Luhan has saved $$ R19800 $$ for a vacation, and the exchange rate is $$ \$1:R15.76 $$. We need to find out how many dollars he can spend.

1. **Calculating the amount in dollars**:
   $$
   \text{Amount in dollars} = \frac{19800}{15.76}
   $$

Let's calculate this value.

### Problem 3.6
Johan weighs twice as much as Melissa, and Lian weighs $$ 1.5 $$ times more than Johan. The total weight of Johan, Melissa, and Lian is $$ 180 \, \text{kg} $$.

1. **Let $$ m $$ be the weight of Melissa**.
   - Then Johan's weight $$ j = 2m $$.
   - Lian's weight $$ l = 1.5j = 1.5(2m) = 3m $$.

2. **Setting up the equation**:
   $$
   m + j + l = 180
   $$
   $$
   m + 2m + 3m = 180
   $$
   $$
   6m = 180
   $$
   $$
   m = 30
   $$

3. **Finding Johan's weight**:
   $$
   j = 2m = 2 \times 30 = 60 \, \text{kg}
   $$

Now, let's calculate the amount in dollars for Problem 3.5.

I'll perform the calculations for Problem 3.5 and summarize the results.
Calculate the value by following steps:
- step0: Calculate:
  $$2\times 30$$
- step1: Multiply the numbers:
  $$60$$
Calculate or simplify the expression $$ 19800 / 15.76 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{19800}{15.76}$$
- step1: Convert the expressions:
  $$\frac{19800}{\frac{394}{25}}$$
- step2: Multiply by the reciprocal:
  $$19800\times \frac{25}{394}$$
- step3: Reduce the numbers:
  $$9900\times \frac{25}{197}$$
- step4: Multiply:
  $$\frac{9900\times 25}{197}$$
- step5: Multiply:
  $$\frac{247500}{197}$$
### Summary of Results

#### Problem 3.4
- **3.4.1**: The length of each piece of bread is $$ 5 \, \text{cm} $$.
- **3.4.2**: The total number of pieces of bread is $$ 13 $$.

#### Problem 3.5
- The amount Luhan can spend on his vacation is approximately $$ 1256.35 \, \text{USD} $$.

#### Problem 3.6
- Johan's weight is $$ 60 \, \text{kg} $$.

If you have any further questions or need additional assistance, feel free to ask!
Each piece of bread is 5 cm long. There are 13 pieces of bread, so 13 people can eat one piece each. Luhan can spend approximately \$1,256.35 on his vacation. Johan weighs 60 kg.

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