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Kaylis [27]
3 years ago
6

a boy is three years younger than his sister. two years ago he was two-thirds of his sister's age. what are their present ages ​

Business
1 answer:
padilas [110]3 years ago
5 0

Answer:

The boy: 8 years old

The sister: 11 years old

Explanation:

We assume that the age at present of the boy is x (years old).

As he is younger than his sister 3 years, so that his sister's present age is great than x 3 years

=> Her present age is: x + 3 (years old)

Two years ago, the boy is younger than present two years

=> The boy's age two years ago is: x - 2 (years old)

Similarly, the sister's age two years ago is: (x+3)-2 = x + 1 (years old)

As given, two years ago he was two-thirds of his sister's age, so that we have:

<em>The boy's age two years ago = </em>\frac{2}{3}<em> × the sister's age two years ago</em>

⇒ x - 2 = \frac{2}{3}(x+1)

⇒ x - 2 = \frac{2}{3}x + \frac{2}{3}

⇒ x - \frac{2}{3}x =  \frac{2}{3} + 2

⇒ \frac{1}{3} x = \frac{8}{3}

⇒ x = \frac{8}{3}. 3 = 8

=> x + 3 = 8 + 3 = 11

So the present age of the boy is 8 years old, of the sister is 11 years old

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