Exercise 114 1. A car use 20 litres of petrol to travel 400 km . Find the rate in litres per km . 2. Calculate the price of milk per litre if a dairy charges $$ \mathrm{R} 42,50 $$ for $$ S $$ litres of milk. 3. To decide which tin of coffee is better value for moncy, calculate the price per gram of a 250 g tin of coffee for R29,49 and a 750 g tin of coffee for R 69,99 .

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

### Part 1: Car Petrol Consumption
1. **Known Conditions:**
   - Petrol used: $$ 20 $$ litres
   - Distance traveled: $$ 400 $$ km

2. **Finding the rate in litres per km:**
   - The rate can be calculated using the formula:
     $$
     \text{Rate} = \frac{\text{Litres}}{\text{Distance}}
     $$
   - Substituting the known values:
     $$
     \text{Rate} = \frac{20}{400}
     $$

### Part 2: Price of Milk per Litre
1. **Known Conditions:**
   - Total price for $$ S $$ litres of milk: $$ R 42.50 $$

2. **Finding the price per litre:**
   - The price per litre can be calculated using the formula:
     $$
     \text{Price per litre} = \frac{\text{Total Price}}{\text{Litres}}
     $$
   - Substituting the known values:
     $$
     \text{Price per litre} = \frac{42.50}{S}
     $$

### Part 3: Price per Gram of Coffee
1. **Known Conditions:**
   - Price of 250 g tin: $$ R 29.49 $$
   - Price of 750 g tin: $$ R 69.99 $$

2. **Finding the price per gram for each tin:**
   - For the 250 g tin:
     $$
     \text{Price per gram} = \frac{29.49}{250}
     $$
   - For the 750 g tin:
     $$
     \text{Price per gram} = \frac{69.99}{750}
     $$

Now, let's perform the calculations for each part.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{42.5}{S}$$
- step1: Rewrite the expression:
  $$\frac{\frac{85}{2}}{S}$$
- step2: Multiply by the reciprocal:
  $$\frac{85}{2}\times \frac{1}{S}$$
- step3: Multiply the terms:
  $$\frac{85}{2S}$$
Calculate or simplify the expression $$ 20/400 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{20}{400}$$
- step1: Reduce the fraction:
  $$\frac{1}{20}$$
Calculate or simplify the expression $$ 69.99/750 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{69.99}{750}$$
- step1: Convert the expressions:
  $$\frac{\frac{6999}{100}}{750}$$
- step2: Multiply by the reciprocal:
  $$\frac{6999}{100}\times \frac{1}{750}$$
- step3: Reduce the numbers:
  $$\frac{2333}{100}\times \frac{1}{250}$$
- step4: Multiply the fractions:
  $$\frac{2333}{100\times 250}$$
- step5: Multiply:
  $$\frac{2333}{25000}$$
Calculate or simplify the expression $$ 29.49/250 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{29.49}{250}$$
- step1: Convert the expressions:
  $$\frac{\frac{2949}{100}}{250}$$
- step2: Multiply by the reciprocal:
  $$\frac{2949}{100}\times \frac{1}{250}$$
- step3: Multiply the fractions:
  $$\frac{2949}{100\times 250}$$
- step4: Multiply:
  $$\frac{2949}{25000}$$
### Solutions

#### Part 1: Car Petrol Consumption
- The rate of petrol consumption is:
  $$
  \text{Rate} = \frac{20}{400} = 0.05 \text{ litres per km}
  $$

#### Part 2: Price of Milk per Litre
- The price per litre of milk is:
  $$
  \text{Price per litre} = \frac{42.50}{S} \text{ R per litre}
  $$

#### Part 3: Price per Gram of Coffee
- For the 250 g tin:
  $$
  \text{Price per gram} = \frac{29.49}{250} \approx 0.11796 \text{ R per gram}
  $$
- For the 750 g tin:
  $$
  \text{Price per gram} = \frac{69.99}{750} \approx 0.09332 \text{ R per gram}
  $$

### Summary of Results
1. The rate of petrol consumption is $$ 0.05 $$ litres per km.
2. The price of milk per litre is $$ \frac{42.50}{S} $$ R.
3. The price per gram of coffee is approximately:
   - $$ 0.11796 $$ R for the 250 g tin.
   - $$ 0.09332 $$ R for the 750 g tin.

From the coffee prices, the 750 g tin offers better value for money.
1. The car uses 0.05 litres of petrol per kilometre. 2. The price of milk is $$ \frac{42.50}{S} $$ R per litre. 3. The 750 g tin of coffee is better value at approximately 0.093 R per gram compared to the 250 g tin at about 0.118 R per gram.

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