Question

Amy is 5 years older than her sister Julie. If the product of their ages is 6. Find the age of Julie.
A. 1 years
B. 2 years
C. 3 years
D. 4 years

Answer 1

Hint: First assume the age of Julie is $x$. Now, we will get that Amy’s age will be 5+x. Then, we use the given information that the product of their ages is 6 to form an equation. Then, solve the quadratic equation in x using the factorisation method to get the answer.

Complete step by step solution:
We have given that Amy is 5 years older than her sister Julie. Let the age of Julie be $x$.
Now the age of Amy will be $5+x$.
Now, we have given that the product of their ages is 6.
So, when we write it in mathematical form we get
$x\left( x+5 \right)=6$
When we simplify this equation we get
$\begin{align}
  & {{x}^{2}}+5x=6 \\
 & {{x}^{2}}+5x-6=0 \\
\end{align}$
We know that the above equation is a quadratic equation of the form $a{{x}^{2}}+bx+c=0$. Now, we solve this equation by using factorization method. In this method we use hot and trial method to factorize polynomial. In hit and trial method we substitute the value of $x$ by any integer and any number that satisfy the equation.

\[\begin{align}
  & {{x}^{2}}+5x-6=0 \\
 & {{x}^{2}}+6x-x-6=0 \\
 & x\left( x+6 \right)-1\left( x+6 \right)=0 \\
 & \left( x+6 \right)\left( x-1 \right)=0 \\
 & \left( x+6 \right)=0\text{ or }\left( x-1 \right)=0 \\
 & x=-6\text{ or }x=1 \\
\end{align}\]
When we solve the above equation we get two values of $x$. As $x$ is age we take the positive value of $x$. So the age of Julie is $1$ year.
The correct answer is option A.

Note: Here in this question we use factorization method to solve quadratic equation. Alternatively we will use square root formula method to solve the quadratic equation. The square root formula for the equation is $a{{x}^{2}}+bx+c=0$ is given by $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.