Question

Sue is 7 years older than Bob. Three less than twice Bob's is Sue age, find bob and Sue's ages now?

Answer 1

Let the present age of Sue and Bob be x and y respectively.

According to first condition,

x = y + 7......(i)

According to second condition,

x = 2y - 3 ...... (ii)

Since, equation (i) = equation (ii),

(x = 7y) = (x = 2y - 3)

$\mathsf{(\cancel{x} = y + 7) = (\cancel{x} = 2y - 3)}$

y + 7 = 2y - 3

y - 2y = - 3 - 7

- y = - 10

$\mathsf{\cancel{-}y = \cancel{-} 10}$

$\fbox{\bold{\mathsf{y = 10}}}$

Substituting y = 10 in equation 1,

x = y + 7

x = 10 + 7

$\fbox{\bold{\mathsf{x = 17}}}$

Therefore, the present age of Sue is 17 years and the present age of Bob is 10 years.