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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?
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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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