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Michael and Elizabeth are competing on a quiz app.
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Michael has 40 points already and is winning 20 points per minute.
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Elizabeth has 20 points already and is winning 25 points per minute.
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Write an equation that can be used to find π, the number of minutes until Elizabeth overtakes Michael.
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As Michael has 40 points already and is winning 20 points per minute, his total points will be given by 40 plus 20π.
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Elizabeth has 20 points already and is winning 25 points per minute.
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Therefore, her total points will be given by 20 plus 25π.
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This means that the equation that can be used to find the number of minutes until Elizabeth overtakes Michael is 20 plus 25π is equal to 40 plus 20π.
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Whilst we werenβt ask to solve this equation, we could do so using the balancing method.
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Subtracting 20 from both sides of the equation gives us 25π is equal to 20 plus 20π.
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Subtracting 20π from both sides of this new equation gives us five π is equal to 20.
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And finally, dividing both sides of this by five gives us π is equal to four.
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This means that, after four minutes, both players, Michael and Elizabeth, will be on 120 points.
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After this point, Elizabeth will overtake Michael.