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
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Explanatory Answer
Let the initial quantity of grains be x kg.
Step 1: First customer
Grains sold = (1/2)x + 3
Remaining grains = x - [(1/2)x + 3] = (1/2)x - 3
Step 2: Second customer
Grains sold = (1/2)((1/2)x - 3) + 3 = (1/4)x - 3/2 + 3 = (1/4)x + 3/2
Remaining grains = ((1/2)x - 3) - ((1/4)x + 3/2) = (1/4)x - 9/2
Step 3: Third customer
Grains sold = (1/2)((1/4)x - 9/2) + 3 = (1/8)x - 9/4 + 3 = (1/8)x + 3/4
Remaining grains = ((1/4)x - 9/2) - ((1/8)x + 3/4) = 0
Step 4: Solve for x
(1/4)x - 9/2 - 1/8 x - 3/4 = 0
(1/8)x - 21/4 = 0
(1/8)x = 21/4
x = (21/4) * 8 = 42
Answer: Initial quantity of grains = 42 kg
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