4 3.1.2 $$ \frac{1}{4}: \frac{1}{12}: \frac{1}{6} $$ $$ \qquad $$ $$ \qquad $$ (2) 3.2 Calculate the value of $$ x $$ if : $$ 3: 2=21: x $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (2) 3.3 Share 60 oranges amongst 3 Grade 8 learners in the ratio $$ 2: 5: 3 $$. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (3) 3.4 If the ratio of boys to girls in a school is $$ 4: 7 $$ and there are 200 boys, calculate the total number of learners in the school. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (3) 3.5 A jar is filled with R2 - coins and R5 - coins. The ratio of the number of R2 - coins to the ratio of the number of R5 - coins is $$ 5: 7 $$. There are 245 R5 - coins in the jar. 3.5.1 How many R2 - coins are in the jar? $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (3)

Question

UpStudy AI · Accepted Answer

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

### 3.1 Calculate the ratio $$ \frac{1}{4}: \frac{1}{12}: \frac{1}{6} $$

To compare these fractions, we can convert them to a common denominator. The least common multiple (LCM) of the denominators (4, 12, and 6) is 12.

1. Convert each fraction:
   - $$ \frac{1}{4} = \frac{3}{12} $$
   - $$ \frac{1}{12} = \frac{1}{12} $$
   - $$ \frac{1}{6} = \frac{2}{12} $$

2. Now we can express the ratio:
   $$
   \frac{3}{12} : \frac{1}{12} : \frac{2}{12} = 3 : 1 : 2
   $$

### 3.2 Calculate the value of $$ x $$ if $$ 3: 2=21: x $$

To find $$ x $$, we can set up a proportion:
$$
\frac{3}{2} = \frac{21}{x}
$$

Cross-multiplying gives:
$$
3x = 42
$$

Now, divide both sides by 3:
$$
x = 14
$$

### 3.3 Share 60 oranges amongst 3 Grade 8 learners in the ratio $$ 2: 5: 3 $$

First, we need to find the total parts in the ratio:
$$
2 + 5 + 3 = 10 \text{ parts}
$$

Next, we can find the value of one part:
$$
\text{Value of one part} = \frac{60}{10} = 6
$$

Now, we can distribute the oranges:
- First learner: $$ 2 \times 6 = 12 $$
- Second learner: $$ 5 \times 6 = 30 $$
- Third learner: $$ 3 \times 6 = 18 $$

So, the distribution is:
- First learner: 12 oranges
- Second learner: 30 oranges
- Third learner: 18 oranges

### 3.4 If the ratio of boys to girls in a school is $$ 4: 7 $$ and there are 200 boys, calculate the total number of learners in the school.

Let the number of boys be $$ 4x $$ and the number of girls be $$ 7x $$.

Given that $$ 4x = 200 $$:
$$
x = \frac{200}{4} = 50
$$

Now, calculate the number of girls:
$$
7x = 7 \times 50 = 350
$$

Total number of learners:
$$
200 + 350 = 550
$$

### 3.5 A jar is filled with R2 - coins and R5 - coins. The ratio of the number of R2 - coins to the number of R5 - coins is $$ 5: 7 $$. There are 245 R5 - coins in the jar.

#### 3.5.1 How many R2 - coins are in the jar?

Let the number of R2 coins be $$ 5y $$ and the number of R5 coins be $$ 7y $$.

Given that $$ 7y = 245 $$:
$$
y = \frac{245}{7} = 35
$$

Now, calculate the number of R2 coins:
$$
5y = 5 \times 35 = 175
$$

### Summary of Answers:
- **3.1:** $$ 3: 1: 2 $$
- **3.2:** $$ x = 14 $$
- **3.3:** First learner: 12 oranges, Second learner: 30 oranges, Third learner: 18 oranges
- **3.4:** Total learners = 550
- **3.5.1:** R2 coins = 175
- **3.1:** The ratio is 3:1:2. - **3.2:** $$ x = 14 $$. - **3.3:** First learner gets 12 oranges, second learner gets 30 oranges, and third learner gets 18 oranges. - **3.4:** There are 550 learners in total. - **3.5.1:** There are 175 R2 coins in the jar.

Upstudy AI Solution

Answer

Solution

3.1 Calculate the ratio

3.2 Calculate the value of if

3.4 If the ratio of boys to girls in a school is and there are 200 boys, calculate the total number of learners in the school.

3.5 A jar is filled with R2 - coins and R5 - coins. The ratio of the number of R2 - coins to the number of R5 - coins is . There are 245 R5 - coins in the jar.

3.5.1 How many R2 - coins are in the jar?

Summary of Answers:

Beyond the Answer

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