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Aiden visited the fruits garden last weekend and helped farmers count the fruits. There were 60% more watermelons than plums. When 148 fruits were added, the watermelons were increased by 40% and the plums increased by 10%. How many fruits were there at first?

Question

Aiden visited the fruits garden last weekend and helped farmers count the fruits. There were 60% more watermelons than plums. When 148 fruits were added, the watermelons were increased by 40% and the plums increased by 10%. How many fruits were there at first?

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Solution

Let's break down the problem step by step:

  1. Let's assume the number of plums initially was P and the number of watermelons was W. According to the problem, there were 60% more watermelons than plums. So, we can write this as: W = P + 0.6P = 1.6P.

  2. The problem also states that when 148 fruits were added, the watermelons increased by 40% and the plums increased by 10%. This means that 0.4W + 0.1P = 148.

  3. Now we have two equations and two unknowns, so we can solve the system of equations.

  4. Substitute W = 1.6P into the second equation: 0.4(1.6P) + 0.1P = 148, which simplifies to 0.64P + 0.1P = 148, and further simplifies to 0.74P = 148.

  5. Solve for P: P = 148 / 0.74 = 200.

  6. Substitute P = 200 into the first equation to find W: W = 1.6 * 200 = 320.

  7. So, initially, there were 200 plums and 320 watermelons, for a total of 200 + 320 = 520 fruits.

This problem has been solved

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