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.

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.