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# The Ages of Two Sisters Are 11 Years and 14 Years. in How Many Years’ Time Will The Product of Their Ages Be 304? - Mathematics

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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 + x^2 = 304
X^2 + 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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