Question

Susan's brother is 5 years more than as old as Susan. The product of their ages in years is 315. How old is Susan?

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asked 2021-05-09
Susan's brother is 5 years more than as old as Susan. The product of their ages in years is 315. How old is Susan?

Answers (1)

2021-05-10
Step 1
Data analysis Given data,
Statement 1: Susan's brother is 5 years more than as old as Susan.
Statement 2: The product of their ages in years is 315.
Susan's age = ?
Step 2
Let Susan's age be 'x'
Susan's brother age be 'y'
From statement 1,
1) \(y=x+5\)
From statement 2,
\(xy=315\)
Substituting 'y' from equation (1)
\(\Rightarrow\ x(x+5)=315\)
\(\Rightarrow\ x^{2}+5x-315=0\)
The solution for \(ax^{2}+bx+c=0\) is,
\(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)
Substituting \(a=1,\ b=5,\ c=-315\)
\(x=-20.42\) or \(15.42\)
Since age cannot be negative,
\(x=15.42\)
From equation (1),
\(y=x+5=20.42\)
Hence the age of Susan is 15.42 years and Susan's brother is 20.42 years.
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