Jill was given a large jar of jam. She gave one sixth of the jam to Jan. Jill then gave one thirteenth of the remaining jam to Jas. Jill was left with 1 kg of jam.What was the weight, in kg, of the jam in Jill’s jar at the start?
Question
Jill was given a large jar of jam. She gave one sixth of the jam to Jan. Jill then gave one thirteenth of the remaining jam to Jas. Jill was left with 1 kg of jam.What was the weight, in kg, of the jam in Jill’s jar at the start?
Solution
Let's denote the initial amount of jam as X kg.
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After giving one sixth of the jam to Jan, Jill was left with X - X/6 = 5X/6 kg of jam.
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Then, Jill gave one thirteenth of the remaining jam to Jas, which means she was left with 5X/6 - (5X/6)/13 = 12/13 * 5X/6 = 60X/78 = 5X/6.5 kg of jam.
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According to the problem, Jill was left with 1 kg of jam. So, we can set up the equation 5X/6.5 = 1.
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Solving this equation for X gives us X = 1 * 6.5/5 = 1.3 kg.
So, the weight of the jam in Jill’s jar at the start was 1.3 kg.
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