A wheat bag contained 45 kg 500 g of wheat, out of which 29 kg 750 g of wheat was sold. How much of wheat is left in the bag? Out of 7 kg 200 g of grapes, 4 kg 750 g of grapes were... A wheat bag contained 45 kg 500 g of wheat, out of which 29 kg 750 g of wheat was sold. How much of wheat is left in the bag? Out of 7 kg 200 g of grapes, 4 kg 750 g of grapes were spoiled and had to be thrown away. How many kilograms of grapes were left?
Understand the Problem
The question is asking how much wheat is left in a bag after selling a specific amount. It requires the calculation of the remaining quantity of wheat by subtracting the sold amount from the total weight of the wheat. Additionally, the second part of the question addresses how many kilograms of grapes were spoiled and needed to be thrown away, which also involves basic arithmetic.
Answer
Remaining wheat: $15 \text{ kg } 750 \text{ g}$; Remaining grapes: $2 \text{ kg } 450 \text{ g}$.
Answer for screen readers
The remaining wheat is 15 kg 750 g, and the remaining grapes are 2 kg 450 g.
Steps to Solve
- Calculate remaining wheat in the bag
To find how much wheat is left in the bag after selling a specific amount, subtract the amount sold from the total amount in the bag.
Let:
- Total wheat in the bag = 45 kg 500 g
- Wheat sold = 29 kg 750 g
First, convert the total wheat into grams: $$ 45 \text{ kg} = 45000 \text{ g} \quad \text{and} \quad 500 \text{ g} = 500 \text{ g} $$ Total wheat in grams: $$ 45000 \text{ g} + 500 \text{ g} = 45500 \text{ g} $$
Next, convert sold wheat into grams: $$ 29 \text{ kg} = 29000 \text{ g} \quad \text{and} \quad 750 \text{ g} = 750 \text{ g} $$ Total wheat sold in grams: $$ 29000 \text{ g} + 750 \text{ g} = 29750 \text{ g} $$
Now, subtract the sold amount from the total: $$ \text{Remaining wheat} = 45500 \text{ g} - 29750 \text{ g} = 15750 \text{ g} $$
- Convert remaining wheat to kilograms and grams
To convert 15750 grams back to kilograms and grams:
- Total kilograms = $$ \frac{15750}{1000} = 15 \text{ kg} $$
- Remaining grams = $$ 15750 \text{ g} - (15 \text{ kg} \times 1000 \text{ g/kg}) = 750 \text{ g} $$
So, the remaining wheat is 15 kg 750 g.
- Calculate spoiled grapes
Next, for the spoiled grapes, convert the total weight into grams:
- Total grapes = 7 kg 200 g $$ 7 \text{ kg} = 7000 \text{ g} $$ Total grapes in grams: $$ 7000 \text{ g} + 200 \text{ g} = 7200 \text{ g} $$
Subtract the spoiled grapes:
- Spoiled grapes = 4 kg 750 g $$ 4 \text{ kg} = 4000 \text{ g} \quad \text{and} \quad 750 \text{ g} = 750 \text{ g} $$ Total spoiled grapes: $$ 4000 \text{ g} + 750 \text{ g} = 4750 \text{ g} $$
Now calculate the remaining grapes: $$ \text{Remaining grapes} = 7200 \text{ g} - 4750 \text{ g} = 2450 \text{ g} $$
Convert remaining grapes to kilograms and grams: $$ \text{Remaining grapes} = 2 \text{ kg} \quad \text{and} \quad 450 \text{ g} $$
The remaining wheat is 15 kg 750 g, and the remaining grapes are 2 kg 450 g.
More Information
This problem involves basic arithmetic operations like addition and subtraction, as well as conversion between kilograms and grams. Converting weights into a single unit (grams) often simplifies calculations.
Tips
- Forgetting to convert all values to the same unit (grams or kilograms) before performing arithmetic operations.
- Mistaking grams for kilograms which can lead to incorrect results. To avoid this, always check and convert units as necessary.
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