7. A golf club has 144 members, of whom 63 are women. a) What fraction of the members are men? b) Two members of the club are standing for election to be president. Mandisa \( \frac{3}{4} \) of the vote. If \( \frac{1}{3} \) of the members voted, how many votes did Mandisa get? 8. A fuel tank is two-thirds full. Adding 60 more litres will fill the tank. What is the capacity of the tank? 9. Lungile pays \( \frac{2}{5} \) of her salary in income tax. She spends \( \frac{2}{3} \) of what is left on rent, food and transport. If she earns R 6400 per month, how much of her salary does she have left?

Let's solve each part of the problem step by step. ### Problem 7 **a)** To find the fraction of the members that are men, we first need to determine the number of men in the club. - Total members = 144 - Women members = 63 The number of men can be calculated as follows: \[ \text{Men} = \text{Total members} - \text{Women} = 144 - 63 = 81 \] Now, the fraction of members that are men is: \[ \text{Fraction of men} = \frac{\text{Men}}{\text{Total members}} = \frac{81}{144} \] We can simplify this fraction: \[ \frac{81}{144} = \frac{9}{16} \quad (\text{dividing both numerator and denominator by 9}) \] **b)** To find out how many votes Mandisa received, we first need to determine how many members voted. - Total members = 144 - Fraction of members who voted = \( \frac{1}{3} \) The number of members who voted is: \[ \text{Voted} = \frac{1}{3} \times 144 = 48 \] Now, Mandisa received \( \frac{3}{4} \) of the votes: \[ \text{Votes for Mandisa} = \frac{3}{4} \times 48 = 36 \] ### Problem 8 We know that the fuel tank is two-thirds full and that adding 60 liters will fill the tank. Let \( C \) be the capacity of the tank. The amount of fuel currently in the tank is: \[ \text{Current fuel} = \frac{2}{3}C \] After adding 60 liters, the tank will be full: \[ \frac{2}{3}C + 60 = C \] To find \( C \), we can rearrange the equation: \[ 60 = C - \frac{2}{3}C \] \[ 60 = \frac{1}{3}C \] Now, multiplying both sides by 3 gives: \[ C = 180 \] ### Problem 9 Lungile pays \( \frac{2}{5} \) of her salary in income tax. Her salary is R 6400. First, we calculate the amount paid in income tax: \[ \text{Income tax} = \frac{2}{5} \times 6400 = 2560 \] Now, we find out how much is left after tax: \[ \text{Amount left} = 6400 - 2560 = 3840 \] Next, she spends \( \frac{2}{3} \) of what is left on rent, food, and transport: \[ \text{Spent} = \frac{2}{3} \times 3840 = 2560 \] Finally, we calculate how much of her salary she has left: \[ \text{Amount left after spending} = 3840 - 2560 = 1280 \] ### Summary of Answers 1. **Fraction of members that are men:** \( \frac{9}{16} \) 2. **Votes Mandisa received:** 36 3. **Capacity of the tank:** 180 liters 4. **Amount Lungile has left:** R 1280