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.

Please explain how to obtain total number of balls.

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.

To find the total number of balls, we need to analyze the given information and create equations based on the relationships between the different color balls.

Let's assign variables to represent the number of balls for each color:
Let's say the number of red balls = R,
the number of blue balls = B,
the number of green balls = G,
and the number of pink balls = P.

Based on the given information, we can create the following equations:

1) Half the total number of balls are pink:
P = (1/2) * (R + B + G + P) ---- Equation 1

2) One-fourth of the number of green balls equals one-third of the number of blue balls:
(1/4)G = (1/3)B ---- Equation 2

3) The number of pink balls is 4 less than twice the total number of green and blue balls:
P = 2(G + B) - 4 ---- Equation 3

4) The number of green balls is 22 less than the total number of blue and pink balls:
G = (B + P) - 22 ---- Equation 4

We now have a system of four equations (Equations 1-4) that can be solved simultaneously to find the values of R, B, G, and P.

To solve the equations, we can use substitution or elimination methods. Let's use the elimination method:

From Equation 1, we can rewrite it as:
P - (1/2)P = (1/2) * (R + B + G) ---- Equation 1'

Simplifying Equation 1':
(1/2)P = (1/2) * (R + B + G)

Multiplying both sides by 2 to eliminate the fraction:
P = R + B + G ---- Equation 5

Substituting Equation 5 into Equation 3:
R + B + G = 2(G + B) - 4

Simplifying the equation:
R = G - 2 ---- Equation 6

Substituting Equations 5 and 6 into Equation 4:
G = (B + P) - 22

Simplifying the equation:
G = (B + (R + B + G)) - 22
G = 2B + R - 22
G - 2B - R = -22 ---- Equation 7

Substituting Equations 6 and 7 into Equation 2:
(1/4)G = (1/3)B

Simplifying the equation:
(1/4)(G - 2) = (1/3)B
3(G - 2) = 4B
3G - 6 = 4B
3G - 4B = 6 ---- Equation 8

Now we have a system of three equations (Equations 5, 6, and 8) with three variables (R, B, and G).

From here, you can solve this system of equations to find the values of R, B, and G. Once you have these values, you can substitute them into Equation 1 or 3 to find the value of P.

After finding the values of R, B, G, and P, you can add them together to find the total number of balls.