Question

In a bag containing red and white balls half the number of white balls is equal to one third of red balls. Thrice the total number of balls exceeds seven times the number of white balls by 6. How many balls of each colour are there?

Answer 1

Let the number of red balls = x and white balls = y
Given that, half the number of white balls is equal to one-third of red balls.
Therefore
y/2 = x/3
3y = 2x
x = 3y/2

Also given that, thrice the total number of balls exceeds seven times the number of white balls by 6
Total number of balls = x + y
Therefore
3(x + y) - 7y = 6
3x + 3y - 7y = 6
3x - 4y = 6
Substituting the value of x
3 (3y/2) - 4y = 6
9y/2 - 4y = 6
(9y - 8y)/2 = 6
y = 12

x = 3*12/2 = 18

The number of red balls = 18
The number of white balls = 12

Hope this helps you.

Answer 2

Given :-

• Half the number of white balls = One third the number of red balls.
• Three times the number of red balls exceeds seven times the number of white balls by 6.

To Find :-

• Number of balls of each colour.

Solution :-

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

Condition ( 1 ) :

⇒ y/2 = x/3

⇒ 2x - 3y = 0......( 1 )

Condition ( 2 ) :

⇒ 3(x + y) - 7y = 6

⇒ 3x + 3y - 7y = 6

⇒ 3x - 4y = 6.......( 2 )

Equation ( 1 ) × 3 gives,

⇒ 6x - 9y = 0.......( 3 )

Equation ( 2 ) × 2 gives,

⇒ 6x - 8y = 12......( 4 )

Equation ( 3 ) - ( 4 ) gives,

⇒ -y = -12

⇒ y = 12

Substituting the value of y in ( 1 ) gives,

⇒ 2x - 36 = 0

⇒ x = 36/2

⇒ x = 18

Hence,

• Number of red balls = 18.
• Number of white balls = 12.