Answer
Verified
398.1k+ views
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 $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.
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 $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
What organs are located on the left side of your body class 11 biology CBSE
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Which are the major cities located on the river Ga class 10 social science CBSE
What is BLO What is the full form of BLO class 8 social science CBSE