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?

Decimals
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?

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.