At a concert 40% of the audience are children.One third of the rest of the audience are men.There are 120 women in the audience.Work out the total number of people in the audience. (3 marks)
Question
At a concert 40% of the audience are children.One third of the rest of the audience are men.There are 120 women in the audience.Work out the total number of people in the audience. (3 marks)
Solution
Sure, let's solve this step by step:
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Let's denote the total number of people in the audience as X.
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According to the problem, 40% of the audience are children. This means that 60% of the audience are adults (100% - 40% = 60%).
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So, the number of adults in the audience is 0.6X.
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The problem also states that one third of the rest of the audience are men. This means that two thirds of the adults are women.
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So, the number of women in the audience is 2/3 * 0.6X = 0.4X.
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We know from the problem that there are 120 women in the audience. So, we can set up the equation 0.4X = 120.
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Solving this equation for X gives us X = 120 / 0.4 = 300.
So, the total number of people in the audience is 300.
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