QUESTION 2 2.1. Jane and Vuyo are sharing profits from their business in the ratio of $$ 4: 3 $$. The business has made a profit of R18 600 this year.Calculate how much each receives. 2.2. Given wants to order mathematics dictionary from the internet. The price of the book is 25.86 dollars. What is the price of the book in rands? Take the exchange rate as 1 dollar for R 9.95 . 2.3. If the ratio of boys in a class of 40 is $$ \frac{6}{8} $$, how many girls are in the class? 2.4. Calculate the final amount that I will have in my savings account if l invest R600 for 2 years at a rate of $$ 6 \% $$ p.a. compound interest.

Question

UpStudy AI · Accepted Answer

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

### 2.1. Profit Sharing

Jane and Vuyo are sharing profits in the ratio of $$ 4:3 $$. The total profit is R18,600.

1. **Calculate the total parts in the ratio:**
   $$
   \text{Total parts} = 4 + 3 = 7
   $$

2. **Calculate the value of one part:**
   $$
   \text{Value of one part} = \frac{18600}{7}
   $$

3. **Calculate Jane's share:**
   $$
   \text{Jane's share} = 4 \times \text{Value of one part}
   $$

4. **Calculate Vuyo's share:**
   $$
   \text{Vuyo's share} = 3 \times \text{Value of one part}
   $$

Now, let's perform the calculations.

### 2.2. Price Conversion

The price of the book is 25.86 dollars, and the exchange rate is 1 dollar for R9.95.

1. **Calculate the price in rands:**
   $$
   \text{Price in rands} = 25.86 \times 9.95
   $$

### 2.3. Ratio of Boys and Girls

The ratio of boys in a class of 40 is $$ \frac{6}{8} $$.

1. **Calculate the total parts in the ratio:**
   $$
   \text{Total parts} = 6 + 8 = 14
   $$

2. **Calculate the number of boys:**
   $$
   \text{Number of boys} = \frac{6}{14} \times 40
   $$

3. **Calculate the number of girls:**
   $$
   \text{Number of girls} = 40 - \text{Number of boys}
   $$

### 2.4. Compound Interest Calculation

If R600 is invested for 2 years at a rate of $$ 6\% $$ p.a. compound interest, we can use the formula for compound interest:

$$
A = P(1 + r)^n
$$

Where:
- $$ A $$ = final amount
- $$ P $$ = principal amount (R600)
- $$ r $$ = interest rate (0.06)
- $$ n $$ = number of years (2)

Now, let's perform all the calculations in parallel.
Calculate the value by following steps:
- step0: Calculate:
  $$25.86\times 9.95$$
- step1: Multiply the numbers:
  $$257.307$$
Calculate or simplify the expression $$ 18600 / 7 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{18600}{7}$$
Calculate or simplify the expression $$ 600 * (1 + 0.06)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$600\left(1+0.06\right)^{2}$$
- step1: Add the numbers:
  $$600\times 1.06^{2}$$
- step2: Convert the expressions:
  $$600\left(\frac{53}{50}\right)^{2}$$
- step3: Evaluate the power:
  $$600\times \frac{2809}{2500}$$
- step4: Multiply:
  $$\frac{16854}{25}$$
Calculate or simplify the expression $$ (6 / 14) * 40 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{6}{14}\right)\times 40$$
- step1: Reduce the fraction:
  $$\frac{3}{7}\times 40$$
- step2: Multiply:
  $$\frac{3\times 40}{7}$$
- step3: Multiply:
  $$\frac{120}{7}$$
Let's summarize the results of each part of the problem:

### 2.1. Profit Sharing
1. **Value of one part:**
   $$
   \text{Value of one part} = \frac{18600}{7} \approx 2657.14
   $$

2. **Jane's share:**
   $$
   \text{Jane's share} = 4 \times 2657.14 \approx 10628.57
   $$

3. **Vuyo's share:**
   $$
   \text{Vuyo's share} = 3 \times 2657.14 \approx 7971.43
   $$

### 2.2. Price Conversion
1. **Price in rands:**
   $$
   \text{Price in rands} = 25.86 \times 9.95 \approx 257.31
   $$

### 2.3. Ratio of Boys and Girls
1. **Number of boys:**
   $$
   \text{Number of boys} = \frac{6}{14} \times 40 \approx 17.14 \quad (\text{approximately } 17)
   $$

2. **Number of girls:**
   $$
   \text{Number of girls} = 40 - 17 \approx 23
   $$

### 2.4. Compound Interest Calculation
1. **Final amount:**
   $$
   A = 600 \times (1 + 0.06)^2 \approx 674.16
   $$

### Final Answers:
- **2.1:** Jane receives approximately R10,628.57 and Vuyo receives approximately R7,971.43.
- **2.2:** The price of the book in rands is approximately R257.31.
- **2.3:** There are approximately 23 girls in the class.
- **2.4:** The final amount in the savings account after 2 years is approximately R674.16.
- **2.1:** Jane receives R10,628.57 and Vuyo receives R7,971.43. - **2.2:** The book costs R257.31. - **2.3:** There are 23 girls in the class. - **2.4:** After 2 years, the savings account will have R674.16.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Arithmetic Questions