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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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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(D) | Q: 4 | Page no. 78
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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? Concept: Quadratic Equations.
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