EXERCISE 44 The price of a television set has been reduced by $$ 10 \% $$ to R799. What was the pre- discount price for this television set? 2. Jacob is a plumber. Due to increased material costs, he puts all his prices up by $$ 7 \% $$. He now charges R320 per hour for his services. What did he charge before he put his prices up? The Natha family are considering flying to Mauritius for a holiday. The total cost of the holiday per person is R12 999 (VAT incl.). What was the price before vat? into her retirement village. She now weighs 81 kg. What was her weight before she moved into her retirement village? The Oliviers are considering buying a second-hand car that has been discounted by 139 . The car is currently selling for R89 000. What was its pre-discount price?

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

### Part 1: Television Set Price

The price of the television set after a $$10\%$$ discount is R799. We need to find the pre-discount price.

Let $$ P $$ be the pre-discount price. The relationship can be expressed as:
$$
P - 0.1P = 799
$$
This simplifies to:
$$
0.9P = 799
$$
Now, we can solve for $$ P $$:
$$
P = \frac{799}{0.9}
$$

### Part 2: Jacob's Plumbing Charges

Jacob increased his prices by $$7\%$$ and now charges R320 per hour. We need to find his previous charge.

Let $$ C $$ be the original charge. The relationship can be expressed as:
$$
C + 0.07C = 320
$$
This simplifies to:
$$
1.07C = 320
$$
Now, we can solve for $$ C $$:
$$
C = \frac{320}{1.07}
$$

### Part 3: Natha Family Holiday Cost

The total cost of the holiday per person is R12,999 (including VAT). We need to find the price before VAT. Assuming VAT is $$15\%$$, the relationship can be expressed as:
$$
P + 0.15P = 12999
$$
This simplifies to:
$$
1.15P = 12999
$$
Now, we can solve for $$ P $$:
$$
P = \frac{12999}{1.15}
$$

### Part 4: Oliviers' Car Price

The car is currently selling for R89,000 after a discount of R13,900. We need to find the pre-discount price.

Let $$ D $$ be the pre-discount price. The relationship can be expressed as:
$$
D - 13900 = 89000
$$
Now, we can solve for $$ D $$:
$$
D = 89000 + 13900
$$

Now, let's perform the calculations for each part.
Calculate the value by following steps:
- step0: Calculate:
  $$89000+13900$$
- step1: Add the numbers:
  $$102900$$
Calculate or simplify the expression $$ 12999 / 1.15 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{12999}{1.15}$$
- step1: Convert the expressions:
  $$\frac{12999}{\frac{23}{20}}$$
- step2: Multiply by the reciprocal:
  $$12999\times \frac{20}{23}$$
- step3: Multiply:
  $$\frac{12999\times 20}{23}$$
- step4: Multiply:
  $$\frac{259980}{23}$$
Calculate or simplify the expression $$ 320 / 1.07 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{320}{1.07}$$
- step1: Convert the expressions:
  $$\frac{320}{\frac{107}{100}}$$
- step2: Multiply by the reciprocal:
  $$320\times \frac{100}{107}$$
- step3: Multiply:
  $$\frac{320\times 100}{107}$$
- step4: Multiply:
  $$\frac{32000}{107}$$
Calculate or simplify the expression $$ 799 / 0.9 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{799}{0.9}$$
- step1: Convert the expressions:
  $$\frac{799}{\frac{9}{10}}$$
- step2: Multiply by the reciprocal:
  $$799\times \frac{10}{9}$$
- step3: Multiply:
  $$\frac{799\times 10}{9}$$
- step4: Multiply:
  $$\frac{7990}{9}$$
Here are the results for each part of the exercise:

### Part 1: Television Set Price
The pre-discount price $$ P $$ is calculated as:
$$
P = \frac{799}{0.9} \approx 887.78
$$
So, the pre-discount price of the television set was approximately **R887.78**.

### Part 2: Jacob's Plumbing Charges
The original charge $$ C $$ is calculated as:
$$
C = \frac{320}{1.07} \approx 299.07
$$
Thus, Jacob charged approximately **R299.07** per hour before the price increase.

### Part 3: Natha Family Holiday Cost
The price before VAT $$ P $$ is calculated as:
$$
P = \frac{12999}{1.15} \approx 11303.48
$$
Therefore, the price before VAT was approximately **R11,303.48**.

### Part 4: Oliviers' Car Price
The pre-discount price $$ D $$ is calculated as:
$$
D = 89000 + 13900 = 102900
$$
Thus, the pre-discount price of the car was **R102,900**.

In summary:
1. Television set pre-discount price: **R887.78**
2. Jacob's original charge: **R299.07**
3. Holiday cost before VAT: **R11,303.48**
4. Car pre-discount price: **R102,900**
- **Television Set:** R887.78 - **Jacob's Charge:** R299.07 - **Holiday Cost Before VAT:** R11,303.48 - **Car Pre-Discount Price:** R102,900

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