Question

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?

Answer 1

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

Answer 2

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