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 discriminant of the equation $3x^{2}-2x+\frac{1}{3}=0$ and hence find the nature of its roots. Find them,if they are real.
Medium
View Solution$A$ prayer hall has a carpet area of $300 \ m^2$ with its length one metre more than twice its breadth. Find the dimensions of the prayer hall.
Difficult
View SolutionFind the roots of the quadratic equation by applying the quadratic formula:
$2x^{2} + x + 4 = 0$
$2x^{2} + x + 4 = 0$
Medium
View SolutionRepresent the following situation in the form of a quadratic equation:
$A$ train travels a distance of $480 \, km$ at a uniform speed. If the speed had been $8 \, km/h$ less,then it would have taken $3 \, hours$ more to cover the same distance. We need to find the speed of the train.
$A$ train travels a distance of $480 \, km$ at a uniform speed. If the speed had been $8 \, km/h$ less,then it would have taken $3 \, hours$ more to cover the same distance. We need to find the speed of the train.
Medium
View SolutionIs the following situation possible? If so,determine their present ages. The sum of the ages of two friends is $20$ years. Four years ago,the product of their ages in years was $48$.
Medium
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