Question

In a bag containing white and red balls, half the number of white balls is equal to one
third the number of red balls. Twice the total number of balls exceeds three times the
number of red balls by 8. How many balls of each type does the bag contain?

Answer 1

Step-by-step explanation:

Let x be the number of white balls and y be the number of black balls.

x/2 = y/3.

Or x = 2y/3.

Again 2 (x+y) = 3y+4.

Or 2x + 2y = 3y + 4.

Or 2x = 3y - 2y + 4

Or 2x = y + 4

Or 2 (2y/3) = y + 4.

Or 4y/3 - y = 4

Or y/3 = 4

Or y = 12.

Now x = 2y/3.

Or x = 24/3 = 8.

Therefore total number of black balls is 12 and number of white balls is 8.

Answer 2

Answer:

white balls are 16 and red balls are 24

Step-by-step explanation:

let the white balls be x

and the red balls be y

Now,

from the given condition ,

x/2 = y/3

x = 2y/3 --------------(1)

2(x + y) = 3y + 8

2x + 2y = 3y + 8

2x - y = 8 –------------(2)

Now , put equation (1) in (2)

2 × (2y/3) - y = 8

4y/3 - y = 8

4y - 3y/3 = 8

y/3 = 8

y = 8 × 3

y = 24 ----------------(3)

Now,put equation (3) in (2)

2x - y = 8

2x - 24 = 8

2x = 8 + 24

2x = 32

x = 32/2

x = 16

ANS: No. of white balls are 16

and No. of red balls are 24