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16 Sep 2014, 00:43
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Two sacks collectively held 40 kilograms of sugar. After transferring 1 kilogram of sugar from the first sack to the second, the weight of the sugar in the first sack became 60% of that in the second. What was the initial weight difference between the two sacks?
A. 4
B. 6
C. 8
D. 10
E. 12
A. 4
B. 6
C. 8
D. 10
E. 12
16 Sep 2014, 00:43
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Official Solution:
Two sacks collectively held 40 kilograms of sugar. After transferring 1 kilogram of sugar from the first sack to the second, the weight of the sugar in the first sack became 60% of that in the second. What was the initial weight difference between the two sacks?
A. 4
B. 6
C. 8
D. 10
E. 12
Let's assume the weight of the second sack after the change is \(x\) kilograms. Then, the weight of the first sack after the change is \(0.6x\). Given that the total weight of sugar in both sacks remains unchanged, we can write the equation \(x + 0.6x = 40\). Solving for \(x\), we find \(x = 25\) kilograms.
Considering that the weight of the second sack after the change is 25 kilograms, its initial weight must have been \(25 - 1 = 24\) kilograms. Consequently, the initial weight of the first sack was \(40 - 24 = 16\) kilograms. Therefore, the original weight difference between the sacks was \(24 - 16 = 8\) kilograms.
Answer: C
Two sacks collectively held 40 kilograms of sugar. After transferring 1 kilogram of sugar from the first sack to the second, the weight of the sugar in the first sack became 60% of that in the second. What was the initial weight difference between the two sacks?
A. 4
B. 6
C. 8
D. 10
E. 12
Let's assume the weight of the second sack after the change is \(x\) kilograms. Then, the weight of the first sack after the change is \(0.6x\). Given that the total weight of sugar in both sacks remains unchanged, we can write the equation \(x + 0.6x = 40\). Solving for \(x\), we find \(x = 25\) kilograms.
Considering that the weight of the second sack after the change is 25 kilograms, its initial weight must have been \(25 - 1 = 24\) kilograms. Consequently, the initial weight of the first sack was \(40 - 24 = 16\) kilograms. Therefore, the original weight difference between the sacks was \(24 - 16 = 8\) kilograms.
Answer: C
01 Jun 2016, 11:29
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x = sack 1 qty in kgs
y = sack 2 qty in kgs
x+y = 40 --- equation 1
(x-1) = 60/100 (y+1) => 5x - 3y = 8
Solve for x , we get x = 16 and hence y = 24. Difference is 8KGS.
y = sack 2 qty in kgs
x+y = 40 --- equation 1
(x-1) = 60/100 (y+1) => 5x - 3y = 8
Solve for x , we get x = 16 and hence y = 24. Difference is 8KGS.
