Answer:
63 tons
Step-by-step explanation:
The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.
The amount remaining in the first pit is 90-x.
The amount remaining in the second pit is 75 -x/3.
Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...
... 90 -x = (1/2)(75 -x/3)
... 180 -2x = 75 -x/3 . . . . multiply by 2
... 105 - 2x = -x/3 . . . . . . subtract 75
... 315 -6x = -x . . . . . . . . multiply by 3
... 315 = 5x . . . . . . . . . . . add 6x
... 63 = x . . . . . . . . . . . . . divide by 5
63 tons of hay were taken from the first pit.
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Check
After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.
