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patriot [66]
3 years ago
7

In a beauty contest,half th number of the experts voted for Mr A and two thirds voted for Mr B.10 voted for both and 6 did not v

ote for either.How many experts were there in all?​

Mathematics
1 answer:
kakasveta [241]3 years ago
7 0

Answer

24 experts

Step-by-step explanation:

As shown in the diagram,we let

U=[Total number of experts who voted]

\implies n(U)=x

This implies that the number of experts who voted for Mr A in terms of x is

\frac{1}{2}x

And in terms of x, the number of experts who voted for Mr B is

\frac{2}{3}x

From the diagram, we can write the below equation,

x= \frac{1}{2}x - 10 + 10 +  \frac{2}{3}x - 10 + 6

x -  \frac{1}{2}x -  \frac{2}{3}x = 4

We multiply through by the L.C.M (is that 6) to get,

6x - 3x - 2x = 24

x = 24

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