Question

A factory produced a total of 850 pink and blue hairclips. 1/3 of the pink hairclips and 100 of the blue hairclips were sold. There was an equal number of pink and blue hairclips left in the end. Express the ratio of the number of pink hairclips to blue hairclips at first.

Answer 1

b + p = 850 so b = 850 - p
(2/3) p = b-100
(2/3) p = 850 - p - 100
(2/3)p = 750 - p
(5/3) p = 750
p = 3 * 150 = 450
so b = 400
p/b = 45/40 = 1.125

Answer 2

There was an error in the equations
Here is the correct answer
b + p = 850 so b = 850 - p
(2/3) p = b-100
(2/3) p = 850 - p - 100
(2/3)p = 750 - p
(5/3) p = 750
p = 3 * 150 = 450
so b = 400
p/b = 450/400 = 9/8
9:8 is the ratio of pink hairclips to blue hairclips at first