Julian, Majid and Pillay had the same number of rubber bands. During a game, Julian lost 12 rubber bands to Pillay and Majid lost 20 rubber bands to Pillay. The ratio of Julian's rubber bands to Majid's rubber bands became 4:3. How many rubber bands did each boy have at first?
Before game:
Julian --- x bands
Majid --- x
Pillay ----x
after game:
Julian ---- x-12
Majid --- x-20
Pillay --- x + 32
(x-12) : (x-20) = 4 : 3
4x - 80 = 3x - 36
x = 44
each had 44
check:
44-12 : 44-20
= 32 ; 24
= 4:3
To solve this problem, we can start by assuming that Julian, Majid, and Pillay initially had the same number of rubber bands, let's say x.
After Julian lost 12 rubber bands to Pillay, Julian will have x - 12 rubber bands and Pillay will have x + 12 rubber bands.
Similarly, after Majid lost 20 rubber bands to Pillay, Majid will have x - 20 rubber bands and Pillay will have x + 32 rubber bands.
We are given that the ratio of Julian's rubber bands to Majid's rubber bands becomes 4:3. This means that the difference in the number of rubber bands between Julian and Majid is 4 - 3 = 1.
From the information above, we can set up the following equation:
(x - 12) / (x - 20) = 4/3
To solve this equation, we can cross-multiply:
3(x - 12) = 4(x - 20)
Simplifying the equation:
3x - 36 = 4x - 80
Rearranging terms:
4x - 3x = 80 - 36
x = 44
Therefore, initially, Julian, Majid, and Pillay each had 44 rubber bands.