A bag has balls of four colours - red,blue,green and pink.Half the total number of balls are pink. One-fourth of the number of green balls equals one-third of the numher of blue balls. The number of pink balls is 4 less than twice the total number of green and blue balls. The number of green balls is 22 less than the total number of blue and pink balls. Find the total number of balls.

Question

Please explain how to obtain total number of balls.

Answer 1

Just translate the English into Math

"Half the total number of balls are pink. "
----> p = (1/2)(r+b+g+p)
2p = r+b+g+p
p = r+b+g , #1

"One-fourth of the number of green balls equals one-third of the numher of blue balls. "
----> (1/4)g = (1/3)b
3g = 4b
g = 4b/3 , #2

"The number of pink balls is 4 less than twice the total number of green and blue balls."
---> p = 2(g+b) - 4
p = 2g + 2b - 4 , #3

"The number of green balls is 22 less than the total number of blue and pink balls. "
---> g = b+p -22 , #4

I have 4 equations with 4 unknowns, so we should be able to solve

From #1 and #3
2g + 2b - 4 = r+b+g
r = b + g - 4 , #5

from #2
g = 4b/3 , #6

#6 with #4
4b/3 = b+p-22
4b = 3b + 3p - 66
b = 3p-66 , #7

back in #1
p = r + b + g
p = b+g-4 + b + b+p-22
26 = 3b+g , but g = 4b/3
26 = 3b + 4b/3
78 = 9b+4b
b = 6

g = 4b/3 = 4(6/3)
g = 8

r = b+g-4
r = 6+8-4 = 10

p = r+b+g = 10+6+8 = 24

red = 10
blue = 6
green = 8
pink = 24
total = 48

All conditions are met

The steps I took of course are not unique, you just keep subbing things all over the place and hope for the best.