ACTIVITY 4 DETERMINE ORIGINAL VALUE 1. The value of an item after $$ 15 \% $$ VAT was added is R 155,50 . What was the value of the item before VAT was added? 2. During 2022 the price of an article increased by $$ 7,5 \% $$ to R 3350,00 . What was the price of the article before the increase? 3. Sello received a $$ 5,5 \% $$ increase in his salary. His salary after the increase was R 35500 . What was his salary before the increase? 4. Due to inflation, the price of bread increased by $$ 4,5 \% $$ to R 16,99 . Calculate the price of the bread before the increase due to inflation. 5. House prices in KwaZulu-Natal increased on average by $$ 18 \% $$ from 2006 to 2007 . If a house cost R 680000 in 2008 , how much would that same house have cost in 2006 ? A bicycle costs R 755,00 including VAT. If VAT is $$ 15 \% $$ how much VAT is included in the price of the bicycle?

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Let's solve each of the problems step by step.

### Problem 1
**Given:** The value of an item after $$ 15\% $$ VAT is R 155.50.  
**To find:** The value of the item before VAT was added.

Let $$ x $$ be the original value before VAT. The equation can be set up as follows:

$$
x + 0.15x = 155.50
$$

This simplifies to:

$$
1.15x = 155.50
$$

Now, we can solve for $$ x $$:

$$
x = \frac{155.50}{1.15}
$$

### Problem 2
**Given:** The price of an article increased by $$ 7.5\% $$ to R 3350.00.  
**To find:** The price of the article before the increase.

Let $$ y $$ be the original price. The equation is:

$$
y + 0.075y = 3350
$$

This simplifies to:

$$
1.075y = 3350
$$

Now, we can solve for $$ y $$:

$$
y = \frac{3350}{1.075}
$$

### Problem 3
**Given:** Sello received a $$ 5.5\% $$ increase in his salary, and his salary after the increase was R 35500.  
**To find:** His salary before the increase.

Let $$ z $$ be the original salary. The equation is:

$$
z + 0.055z = 35500
$$

This simplifies to:

$$
1.055z = 35500
$$

Now, we can solve for $$ z $$:

$$
z = \frac{35500}{1.055}
$$

### Problem 4
**Given:** The price of bread increased by $$ 4.5\% $$ to R 16.99.  
**To find:** The price of the bread before the increase.

Let $$ w $$ be the original price. The equation is:

$$
w + 0.045w = 16.99
$$

This simplifies to:

$$
1.045w = 16.99
$$

Now, we can solve for $$ w $$:

$$
w = \frac{16.99}{1.045}
$$

### Problem 5
**Given:** House prices increased by $$ 18\% $$ from 2006 to 2007, and a house cost R 680000 in 2008.  
**To find:** The cost of the house in 2006.

Let $$ v $$ be the price in 2006. The equation is:

$$
v + 0.18v = 680000
$$

This simplifies to:

$$
1.18v = 680000
$$

Now, we can solve for $$ v $$:

$$
v = \frac{680000}{1.18}
$$

### Problem 6
**Given:** A bicycle costs R 755.00 including VAT, and VAT is $$ 15\% $$.  
**To find:** How much VAT is included in the price of the bicycle.

Let $$ u $$ be the original price before VAT. The equation is:

$$
u + 0.15u = 755
$$

This simplifies to:

$$
1.15u = 755
$$

Now, we can solve for $$ u $$:

$$
u = \frac{755}{1.15}
$$

Now, let's calculate all the values.
Solve the equation by following steps:
- step0: Solve for $$w$$:
  $$1.045w=16.99$$
- step1: Divide both sides:
  $$\frac{1.045w}{1.045}=\frac{16.99}{1.045}$$
- step2: Divide the numbers:
  $$w=\frac{3398}{209}$$
Solve the equation $$ 1.055z=35500 $$.
Solve the equation by following steps:
- step0: Solve for $$z$$:
  $$1.055z=35500$$
- step1: Divide both sides:
  $$\frac{1.055z}{1.055}=\frac{35500}{1.055}$$
- step2: Divide the numbers:
  $$z=\frac{7100000}{211}$$
Solve the equation $$ 1.15u=755 $$.
Solve the equation by following steps:
- step0: Solve for $$u$$:
  $$1.15u=755$$
- step1: Divide both sides:
  $$\frac{1.15u}{1.15}=\frac{755}{1.15}$$
- step2: Divide the numbers:
  $$u=\frac{15100}{23}$$
Solve the equation $$ 1.15x=155.50 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$1.15x=155.5$$
- step1: Divide both sides:
  $$\frac{1.15x}{1.15}=\frac{155.5}{1.15}$$
- step2: Divide the numbers:
  $$x=\frac{3110}{23}$$
Solve the equation $$ 1.075y=3350 $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$1.075y=3350$$
- step1: Divide both sides:
  $$\frac{1.075y}{1.075}=\frac{3350}{1.075}$$
- step2: Divide the numbers:
  $$y=\frac{134000}{43}$$
Solve the equation $$ 1.18v=680000 $$.
Solve the equation by following steps:
- step0: Solve for $$v$$:
  $$1.18v=680000$$
- step1: Divide both sides:
  $$\frac{1.18v}{1.18}=\frac{680000}{1.18}$$
- step2: Divide the numbers:
  $$v=\frac{34000000}{59}$$
Here are the calculated values for each problem:

### Problem 1
The value of the item before VAT was added:
$$
x = \frac{3110}{23} \approx 135.65
$$

### Problem 2
The price of the article before the increase:
$$
y = \frac{134000}{43} \approx 3116.28
$$

### Problem 3
Sello's salary before the increase:
$$
z = \frac{7100000}{211} \approx 33600.00
$$

### Problem 4
The price of the bread before the increase:
$$
w = \frac{3398}{209} \approx 16.24
$$

### Problem 5
The cost of the house in 2006:
$$
v = \frac{34000000}{59} \approx 576271.19
$$

### Problem 6
The original price of the bicycle before VAT:
$$
u = \frac{15100}{23} \approx 655.22
$$

### VAT Calculation
To find the VAT included in the price of the bicycle:
$$
\text{VAT} = 755 - u \approx 755 - 655.22 \approx 99.78
$$

### Summary of Results
1. Original value before VAT: R 135.65
2. Price before increase: R 3116.28
3. Salary before increase: R 33600.00
4. Price of bread before increase: R 16.24
5. House price in 2006: R 576271.19
6. VAT included in the bicycle price: R 99.78

If you need further assistance or clarification, feel free to ask!
1. The original value before VAT was R 135.65. 2. The price before the increase was R 3116.28. 3. Sello's salary before the increase was R 33600.00. 4. The price of the bread before the increase was R 16.24. 5. The house cost R 576271.19 in 2006. 6. The VAT included in the bicycle price was R 99.78.

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