SOLUTION: Hi boxes a and b contain 112 pencils.when 1/5 of the pencils in box a were transfered to box b, both boxes contained the same number of pencils. how many more pencils were there

Question 983984: Hi
boxes a and b contain 112 pencils.when 1/5 of the pencils in box a were transfered to box b, both boxes contained the same number of pencils.
how many more pencils were there in box a than in box b at first.
THANK YOU
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!

Let x and y be the numbers of pencils in the boxes a and b respectively.

Then you have two equations in two unknowns

x + y = 112,               and

x - x = y + x.

From the second equation

5x - x = 5y + x,     or

3x = 5y.                 (1)

From the first equation

3x + 3y = 336.       (2)

Now, replace 3x in the equation (2) by 5y, according to (1). You will get

5y + 3y = 336,     or

8y = 336,             or

y = = 42.

Now, x = = = = .

Hence, there were 70 pencils in the box a and 42 pencils in the box b.

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