A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
Question:
A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
Options
Answer: 42
Explanation:
Let the initial quantity be x kg. After first sale: sold = (1/2)x + 3, so remaining = x − [(1/2)x + 3] = (1/2)x − 3. After second sale: half of remaining = (1/2)[(1/2)x − 3] = (1/4)x − 3/2. Sold to second = (1/4)x − 3/2 + 3 = (1/4)x + 3/2. Remaining = (1/2)x − 3 − [(1/4)x + 3/2] = (1/4)x − 9/2. After third sale: half of remaining = (1/2)[(1/4)x − 9/2] = (1/8)x − 9/4. Sold to third = (1/8)x − 9/4 + 3 = (1/8)x + 3/4. Remaining = (1/4)x − 9/2 − [(1/8)x + 3/4] = (1/8)x − 21/4. Given nothing is left, set remaining = 0: (1/8)x − 21/4 = 0 ⇒ (1/8)x = 21/4 ⇒ x = 8 × (21/4) = 2 × 21 = 42. Answer: 42 kg
Explanation:
Let the initial quantity be x kg. After first sale: sold = (1/2)x + 3, so remaining = x − [(1/2)x + 3] = (1/2)x − 3. After second sale: half of remaining = (1/2)[(1/2)x − 3] = (1/4)x − 3/2. Sold to second = (1/4)x − 3/2 + 3 = (1/4)x + 3/2. Remaining = (1/2)x − 3 − [(1/4)x + 3/2] = (1/4)x − 9/2. After third sale: half of remaining = (1/2)[(1/4)x − 9/2] = (1/8)x − 9/4. Sold to third = (1/8)x − 9/4 + 3 = (1/8)x + 3/4. Remaining = (1/4)x − 9/2 − [(1/8)x + 3/4] = (1/8)x − 21/4. Given nothing is left, set remaining = 0: (1/8)x − 21/4 = 0 ⇒ (1/8)x = 21/4 ⇒ x = 8 × (21/4) = 2 × 21 = 42. Answer: 42 kg
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