Question

A box contains 1079 counters which are coloured either black, white or red.
The ratio of black counters to white counters is 2:7
The ratio of white counters to red counters is 3 : 8
Calculate the number of red counters that are in the box.
Optional working
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Answer:
red counters.

Answer 1

The total number of red counters that are in the box is; 728 red counters

• We are told that the box contains 1079 counters.

Let the number of white counters be x.

Let the number of red counters be y.

Let the number of black counters be z.

Thus;

z:x = 2:7

Thus; 2x/7 = z

Also, we are given;

x:y = 3:8

Thus;

8x/3 = y

• Since total number in the box is 1079,then;

x + y + z = 1079

x + (8x/3) + (2x/7) = 1079

Multiply through by 21 to get;

21x + 56x + 6x = 22659

83x = 22659

x = 22659/83

x = 273

2x/7 = z

Thus; z = 2 × 273/7

z = 78

8x/3 = y

y = 8 × 273/3

y = 728

• Thus,there are;

273 white counters

728 red counters

78 black counters.

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