Represent the following situation in the form of a quadratic equation:
Rohan's mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohan's present age.
Rohan's mother is $26$ years older than him. The product of their ages (in years) $3$ years from now will be $360$. We would like to find Rohan's present age.
(N/A) Let Rohan's present age be $x$ years.
Then,his mother's present age $= x + 26$ years.
After $3$ years:
Rohan's age $= x + 3$ years.
Mother's age $= (x + 26) + 3 = x + 29$ years.
According to the problem,the product of their ages after $3$ years is $360$.
Therefore,$(x + 3)(x + 29) = 360$.
Expanding the equation: $x^2 + 29x + 3x + 87 = 360$.
$x^2 + 32x + 87 - 360 = 0$.
$x^2 + 32x - 273 = 0$.
Then,his mother's present age $= x + 26$ years.
After $3$ years:
Rohan's age $= x + 3$ years.
Mother's age $= (x + 26) + 3 = x + 29$ years.
According to the problem,the product of their ages after $3$ years is $360$.
Therefore,$(x + 3)(x + 29) = 360$.
Expanding the equation: $x^2 + 29x + 3x + 87 = 360$.
$x^2 + 32x + 87 - 360 = 0$.
$x^2 + 32x - 273 = 0$.
Explore More
Similar Questions
Find the values of $k$ for the following quadratic equation,so that it has two equal roots:
$k x(x-2)+6=0$
$k x(x-2)+6=0$
Medium
View SolutionRepresent the following situation mathematically:
John and Jivanti together have $45$ marbles. Both of them lost $5$ marbles each,and the product of the number of marbles they now have is $124$. We would like to find out how many marbles they had to start with.
John and Jivanti together have $45$ marbles. Both of them lost $5$ marbles each,and the product of the number of marbles they now have is $124$. We would like to find out how many marbles they had to start with.
Easy
View SolutionTwo water taps together can fill a tank in $9 \frac{3}{8}$ hours. The tap of larger diameter takes $10 \text{ hours}$ less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Difficult
View Solution$A$ pole has to be erected at a point on the boundary of a circular park of diameter $13 \, m$ in such a way that the differences of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7 \, m$. Is it possible to do so? If yes,at what distances from the two gates should the pole be erected?
Difficult
View SolutionCheck whether the following is a quadratic equation:
$x^{2}+3x+1=(x-2)^{2}$
$x^{2}+3x+1=(x-2)^{2}$
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo