Question

The product of the ages in years) of two sisters is 238. The difference in
their ages (in years) is 3. We would like to find their present ages.​

Answer 1

Let the ages of the two sisters be x and y respectively.

According to the question,

xy = 238.

Also,

x - y = 3.

x = 3 + y. ....(1)

Substituting the value of x from equation (1).

xy = 238.

(3+y) × y = 238.

3y + y^2 = 238.

y^2 + 3y - 238 = 0.

(arranging)

y^2 +14y -17y - 238 = 0.

( splitting the middle term )

y( y+14 ) - 17 ( y+14) = 0 .

(y+14) (y-17) = 0.

Finding the value of y :

y+14 = 0

y = -14.

y-17 = 0.

y = 17.

So, x = -14 or x = 17.

Since , age cannot be negative, x = 17.

17-y = 3.

17-y = 3.

-y = 3 - 17.

-y = -14 .

y = 14.

Hence, one of the sister is 17 years old and the other sister is 14 years old.

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