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.
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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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