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On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.(2) The number of women on the sight-seeing tour was less than 30.

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ukshedrack

Answer:

Number of men on sight-seeing = 22

Step-by-step explanation:

Let number of women = w

Let number of children = c

Let number of men = m

[tex]\frac{w}{c}=\frac{5}{2}[/tex] (given)

w = 5x and c = 2x for some integer x (since number of people have to be an integer)

Given also that

[tex]\frac{c}{m}=\frac{5}{11}[/tex]

c = 5y and m = 11y for some integer y

The number of women on the tour was less than 30

That is 5x < 30;

x < 6 (After dividing both sides by 5)

But c = 2x and c = 5y.

Since c is a multiple of 5, 2x has to be a multiple of 5 e.g. 10

We got x < 6 earllier

Using x = 5, c = 2*5 = 10

So, 10 = 5y

Dividing both sides by 5

10/5 = 5y/5 ⇒ 2 = y

Number of men, m = 11y = 11*2 = 22

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