3 Skryf 5880 as ' $$ n $$ produk van priemfaktore. 4erdeel R180 in de verhouding 1:6:2 ' $$ n $$ Motoris lê ' $$ n $$ afstand van 60 km af teen ' $$ n $$ spoed van $$ 100 \mathrm{~km} / \mathrm{h} $$. Hoe ver sal hy ry in dleselfde tyd indien hy teen $$ 80 \mathrm{~km} / \mathrm{h} $$ ry. Die verhouding van hokkle seuns tot hokkie dogters is $$ 3: 8 $$ by ' $$ n $$ sportsdag. Indlen daar 40 dogters was, hoeveel leerders was daar in totaal?

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UpStudy AI · Accepted Answer

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

### Part 1: Write 5880 as a product of prime factors.

To express 5880 as a product of prime factors, we will perform prime factorization.

1. Start by dividing 5880 by the smallest prime number, which is 2.
2. Continue dividing by 2 until it is no longer divisible by 2.
3. Move to the next smallest prime number (3, 5, etc.) and repeat the process.

Let's perform the factorization:

- $$ 5880 \div 2 = 2940 $$
- $$ 2940 \div 2 = 1470 $$
- $$ 1470 \div 2 = 735 $$ (no longer divisible by 2)
- $$ 735 \div 3 = 245 $$
- $$ 245 \div 5 = 49 $$
- $$ 49 \div 7 = 7 $$
- $$ 7 \div 7 = 1 $$

Now we can write the prime factorization:

$$
5880 = 2^3 \times 3^1 \times 5^1 \times 7^2
$$

### Part 2: Divide R180 in the ratio 1:6:2.

To divide R180 in the ratio 1:6:2, we first find the total parts of the ratio:

$$
1 + 6 + 2 = 9 \text{ parts}
$$

Now, we can find the value of one part:

$$
\text{Value of one part} = \frac{180}{9} = 20
$$

Now we can find the amounts for each part:

- First part: $$ 1 \times 20 = R20 $$
- Second part: $$ 6 \times 20 = R120 $$
- Third part: $$ 2 \times 20 = R40 $$

So, the amounts are:
- R20, R120, and R40.

### Part 3: Distance traveled at different speeds.

A motorist travels 60 km at a speed of 100 km/h. We need to find out how far he would travel in the same time if he drives at 80 km/h.

First, calculate the time taken to travel 60 km at 100 km/h:

$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{60}{100} = 0.6 \text{ hours}
$$

Now, we will find the distance he can travel at 80 km/h in the same time:

$$
\text{Distance} = \text{Speed} \times \text{Time} = 80 \times 0.6 = 48 \text{ km}
$$

### Part 4: Ratio of boys to girls in a sports day.

The ratio of boys to girls is 3:8. If there are 40 girls, we need to find the total number of learners.

Let the number of boys be $$ b $$ and the number of girls be $$ g $$.

From the ratio, we can express the number of boys in terms of girls:

$$
\frac{b}{g} = \frac{3}{8} \implies b = \frac{3}{8}g
$$

Substituting $$ g = 40 $$:

$$
b = \frac{3}{8} \times 40 = 15
$$

Now, the total number of learners is:

$$
\text{Total} = b + g = 15 + 40 = 55
$$

### Summary of Answers:
1. $$ 5880 = 2^3 \times 3^1 \times 5^1 \times 7^2 $$
2. R20, R120, R40
3. 48 km
4. 55 learners in total.
1. $$ 5880 = 2^3 \times 3 \times 5 \times 7^2 $$ 2. R20, R120, R40 3. 48 km 4. 55 learners in total.

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