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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.

Respuesta :

Answer:

  • 12 black counters

Step-by-step 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
semsee45

Answer:

12

Step-by-step explanation:

Given ratio

yellow : black = 3 : 1

⇒ yellow : black = [tex]3x : x[/tex]

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

[tex]\implies \textsf{yellow - 21: black = 5 : 4}[/tex]

[tex]\implies (3x - 21):x=5:4[/tex]

[tex]\implies \dfrac{3x - 21}{x}=\dfrac54[/tex]

[tex]\implies 4(3x - 21)=5x[/tex]

[tex]\implies 12x-84=5x[/tex]

[tex]\implies7x=84[/tex]

[tex]\implies x=12[/tex]

Substituting [tex]x=12[/tex] into the original ratio:

[tex]\implies \textsf{yellow : black} =3(12) : (12)=36:12[/tex]

So the total number of black counters = 12

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