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Question
The ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
Solution
The ages of two sisters are 11 years and 14 years.
Let in x number of years the product of their ages be 304.
∴ (11 + x)(14 + x) = 304
154 + 11x + 14x + x2 = 304
x2 + 25x – 150 = 0
(x + 30)(x – 5) = 0
x = −30, 5
But, the number of years cannot be negative.
So, x = 5.
Hence, the required number of years is 5 years.
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