Question 1187108: Hi
At a farm 2 more than half of a number of eggs were taken out of a basket. Later 2 fewer than half of the remaining number of eggs were taken out again. If 20 eggs were left,how many were there at first.
Thanks
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! g, 'a number of eggs'
(1)
Eggs remaining, 
(2)
 ------twenty eggs remaining
Simplify and solve for g.
(Maybe start by multiplying both sides of equation by 4).
Answer by ikleyn(52802)  (Show Source):
You can put this solution on YOUR website! .
At a farm 2 more than half of a number of eggs were taken out of a basket.
Later 2 fewer than half of the remaining number of eggs were taken out again.
If 20 eggs were left,how many were there at first.
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Let x be the number of remaining eggs after the first taking out.
About this amount of x, we know that after taking out "2 fewer than half of x"
20 eggs were left.
It gives us an equation to find x
x -  = 20
Multiply both sides by 2 and simplify
2x - (x - 4) = 40,
x = 36.
Now we are in position to determine the original number of eggs, y.
From the problem description, we have the following equation for y
y -  = 36.
Multiply both sides by 2 and simplify
2y - y - 4 = 72
y = 76.
ANSWER. At first, there were 76 eggs.
CHECK. First, 76/2 + 2 = 38+2 = 40 eggs were taken out; 76 - 40 = 36 eggs remained.
Next, 36/2 - 2 = 18-2 = 16 eggs were taken out; 36 - 16 = 20 eggs remained. ! Correct !
Solved.
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This solution is a kind of the backward methodology, although in the hidden/(latent) form.
Answer by MathTherapy(10552)  (Show Source):
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