There were 135 more hangers in wardrobe X than in wardrobe Y.

Question

There were 135 more hangers in wardrobe X than in wardrobe Y.
After 20 hangers were transferred from wardrobe Y to wardrobe X, there were 6 times as many hangers in wardrobe X than in wardrobe Y.
How many hangers were there in wardrobe X at first

Answer 1

1)  x = y + 135

2)  x + 20 = 6(y-20)

 

simplify the 2nd equation:

x + 20 = 6(y-20)

x + 20 = 6y - 120

x - 6y = -140

 

Our system of equations is:

 

1)  x = y + 135

2)  x - 6y = -140

 

Replace x in equation 2 with y + 135

 

(y+135) - 6y = -140

-5y + 135 = -140

-5y = -275

y = 55 hangers

 

x = y + 135 = 190 hangers