Arnold had $120 and Lucy had $36 at first. After they each bought a book for the same price, Lucy had 1/5 as much money as Arnold had. How much did the book cost?
cost of book --- x
after book purchase:
Arnold had 120-x
Lucy had 36-x
36-x = (1/5(120-x)
times 5
180 - 5x = 120-x
-4x = -60
x = 15
the book cost $15
Let price of book = x
money arnold had after buying the book = 120-x
money lucy had after buying the book = 36-x
Money lucy has compared to arnold: 36-x = 1/5(120-x)
36-x = (120-x)/5
multiply both side by 5
5(36-x) = 120-x
180-5x = 120-x
add 5x to both sides
180 = 120 + 4x
180 -120 = 4x
4x = 60
Therefore x = $15. So the price of the book is 15.
Now you can test this value
Money lucy had after buying the book = 36-15 = 21
Money Arnold had after buying the book = 120-15 = 105
And 21 is exactly one-fifth of 105 which is the money arnold had