Question

There are yellow counters and black counters in a bag in the ratio 3:1

21 yellow counters are removed and the ratio becomes 5:4

Work out how many black counters there are in the bag.

Answer 1

• 12 black counters

Explanation:

Let the yellow counters be represented by 'y' and black counters by 'b'.

Originally

• y : b = 3 : 1

After removing 21 counters

• y - 21 : b = 5 : 4

Taking the first ratio, equate it to b.

• y/b = 3
• b = y/3

Now, substitute for 'b' in the second ratio.

• y - 21 / (y/3) = 5/4
• 3 (y - 21) / y = 5/4
• 12 (y - 21) = 5y
• 12y - 252 = 5y
• 7y = 252
• y = 36 yellow counters

Now, to find b :

• b = y/3
• b = 36/3
• b = 12 black counters

Answer 2

12

Explanation:

Given ratio

yellow : black = 3 : 1

⇒ yellow : black =
`3x : x`

If 21 yellow counters are removed and the ratio becomes 5 : 4

`\implies \textsf{yellow - 21: black = 5 : 4}`

`\implies (3x - 21):x=5:4`

`\implies (3x - 21)/(x)=\frac54`

`\implies 4(3x - 21)=5x`

`\implies 12x-84=5x`

`\implies7x=84`

`\implies x=12`

Substituting
`x=12` into the original ratio:

`\implies \textsf{yellow : black} =3(12) : (12)=36:12`

So the total number of black counters = 12