Pregunta
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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?

Ask by Daniels Vaughn. in South Africa
Mar 09,2025

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**Problem 7:** - **a)** \( \frac{9}{16} \) of the members are men. - **b)** Mandisa received 36 votes. **Problem 8:** - The fuel tank's capacity is 180 liters. **Problem 9:** - Lungile has R 1280 left after expenses.

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To tackle the fractions from the first question, we determine the number of men in the golf club first. With 144 members and 63 being women, the number of men is 144 - 63 = 81. Therefore, the fraction of members who are men is \( \frac{81}{144} \), which simplifies to \( \frac{9}{16} \) when we divide both the numerator and denominator by 9. Now, for Mandisa's voting situation, if \( \frac{1}{3} \) of the members vote, that’s \( 144 \div 3 = 48 \) votes. Since Mandisa received \( \frac{3}{4} \) of that, she got \( 48 \times \frac{3}{4} = 36 \) votes. Next on the fuel tank, if adding 60 litres fills it, that means the two-thirds capacity of the tank is 60 litres less than the complete capacity. If we consider \( x \) as the full capacity, then \( \frac{2}{3}x + 60 = x \). Solving that gives us the tank's capacity \( x = 90 \) litres. Now for Lungile's salary, she pays \( \frac{2}{5} \) in income tax, which is \( R 6400 \times \frac{2}{5} = R 2560 \). After tax, she has \( 6400 - 2560 = R 3840 \). She spends \( \frac{2}{3} \) of what’s left on essentials, translating to \( 3840 \times \frac{2}{3} = R 2560 \). Thus, her remaining amount is \( 3840 - 2560 = R 1280 \). So, Lungile has R 1280 left after taxes and expenses.

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