One truck has loaded 1000 kg of watermelons, which consist of 99% water. After a long drive in the sun, the melons consist of only 98% water. How many kilograms of melons has he lo... One truck has loaded 1000 kg of watermelons, which consist of 99% water. After a long drive in the sun, the melons consist of only 98% water. How many kilograms of melons has he loaded now?
Understand the Problem
The question asks us to find out the weight of the watermelons after they have lost some water due to drying in the sun, transitioning from being 99% water to 98% water. We will need to calculate this using the initial weight of the watermelons and the percentage of water content before and after.
Answer
The final weight of the watermelon after drying is \( W_f = 0.5W \).
Answer for screen readers
The final weight of the watermelon after drying is ( W_f = 0.5W ), where ( W ) is the initial weight of the watermelon.
Steps to Solve
- Identify initial conditions
Let’s denote the initial weight of the watermelon as $W$. According to the problem, initially, the watermelons are 99% water, so the weight of the water (water content) can be expressed as:
$$ W_{water_initial} = 0.99W $$
The weight of the solid parts (non-water content) is:
$$ W_{solid} = 0.01W $$
- Determine the final conditions
After drying in the sun, the watermelons become 98% water. The weight of the solid parts remains unchanged, while now we denote the final weight of the watermelon as $W_f$. Therefore, the equation for the new situation can be set up:
$$ W_{solid} = 0.02W_f $$
- Set up the equations
Since we know that the weight of the solids does not change, we can equate the solid weight expressions:
$$ 0.01W = 0.02W_f $$
Now we can solve for $W_f$:
- Solve for the final weight
Rearranging and solving the equation gives:
$$ W_f = \frac{0.01W}{0.02} $$
This simplifies to:
$$ W_f = 0.5W $$
This means that the final weight of the watermelon after drying is half of the initial weight.
The final weight of the watermelon after drying is ( W_f = 0.5W ), where ( W ) is the initial weight of the watermelon.
More Information
This result indicates that when the water content of the watermelon decreases from 99% to 98%, the overall weight of the watermelon is halved, demonstrating the significant impact of water content on the total mass.
Tips
- Assuming the weight of the solid remains constant leads to the correct understanding of the problem.
- Not realizing that the percentage change affects the total weight drastically can lead to misunderstanding.
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