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

Algebra ->  Percentage-and-ratio-word-problems -> 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      Log On


   

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) About Me  (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 - 1%2F5x = y + 1%2F5x.

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 = 336%2F8 = 42.

Now,  x = 5y%2F3 = %285%2A42%29%2F3 = 210%2F3 = 70.

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