A wheat bag contained 45 kg 500 g of wheat, out of which 29 kg 750 g of wheat was sold. How much wheat is left in the bag? Out of 7 kg 200 g of grapes, 4 kg 750 g of grapes were sp... A wheat bag contained 45 kg 500 g of wheat, out of which 29 kg 750 g of wheat was sold. How much wheat is left in the bag? Out of 7 kg 200 g of grapes, 4 kg 750 g of grapes were spoilt and had to be thrown away. How many kilograms of grapes were left?
Understand the Problem
The question is asking us to calculate the amount of wheat left in a bag after a certain quantity is sold, as well as how many kilograms of grapes were spoil. This involves basic arithmetic operations such as subtraction.
Answer
The remaining weight of wheat is $15 \, \text{kg} \, 750 \, \text{g}$, and the spoiled grapes are $2 \, \text{kg} \, 450 \, \text{g}$.
Answer for screen readers
The remaining weight of wheat is $15 , \text{kg} , 750 , \text{g}$ and the spoiled grapes amount to $2 , \text{kg} , 450 , \text{g}$.
Steps to Solve
- Convert all weights to grams
The total weight of wheat in the bag is given as $45 , \text{kg} , 500 , \text{g}$. We convert this to grams:
$$ 45 , \text{kg} = 45000 , \text{g} \ 45 , \text{kg} , 500 , \text{g} = 45000 , \text{g} + 500 , \text{g} = 45500 , \text{g} $$
- Calculate the remaining weight of wheat
Next, we need to subtract the amount of wheat sold, which is $29 , \text{kg} , 750 , \text{g}$. First, we convert this amount to grams:
$$ 29 , \text{kg} = 29000 , \text{g} \ 29 , \text{kg} , 750 , \text{g} = 29000 , \text{g} + 750 , \text{g} = 29750 , \text{g} $$
Now, subtract the sold wheat from the total wheat:
$$ 45500 , \text{g} - 29750 , \text{g} = 15750 , \text{g} $$
- Convert the remaining weight back to kilograms and grams
We need to convert $15750 , \text{g}$ back into kilograms and grams:
$$ 15750 , \text{g} = 15 , \text{kg} , 750 , \text{g} $$
- Calculate the spoiled grapes
The total weight of grapes is $7 , \text{kg} , 200 , \text{g}$, which we convert to grams:
$$ 7 , \text{kg} = 7000 , \text{g} \ 7 , \text{kg} , 200 , \text{g} = 7000 , \text{g} + 200 , \text{g} = 7200 , \text{g} $$
Next, we convert the spoiled grapes, $4 , \text{kg} , 750 , \text{g}$, into grams:
$$ 4 , \text{kg} = 4000 , \text{g} \ 4 , \text{kg} , 750 , \text{g} = 4000 , \text{g} + 750 , \text{g} = 4750 , \text{g} $$
- Calculate the remainder of the grapes
Now, we subtract the spoiled grapes from the total grapes:
$$ 7200 , \text{g} - 4750 , \text{g} = 2450 , \text{g} $$
- Convert remaining grapes to kilograms and grams
Convert the remaining grapes back to kilograms:
$$ 2450 , \text{g} = 2 , \text{kg} , 450 , \text{g} $$
The remaining weight of wheat is $15 , \text{kg} , 750 , \text{g}$ and the spoiled grapes amount to $2 , \text{kg} , 450 , \text{g}$.
More Information
This problem involves basic arithmetic operations and understanding of unit conversions between kilograms and grams. It emphasizes the importance of ensuring consistent units when performing calculations.
Tips
- Failing to convert all weights to the same unit (either all in grams or all in kilograms).
- Not properly subtracting the sold or spoiled amount from the original total.
- Confusing the conversion back from grams to kilograms.
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