Question

From the pair of linear equations in the following problems and find their solutions graphically.

The ages of two girls are in the ratio 5:7.Eight years ago their ages were in the ratio 7:13. Find their present ages

Answer 1

Step1: Framing a relation between the ages of two girls

Let the present age of first girl be $x$ and that of second be $y$ years

Given that ratio of ages $=5:7$.

$\Rightarrow$ $\frac{x}{y}$=$\frac{5}{7}$

$\Rightarrow 7x=5y$ ……………………………..(1)

Step 2: Conditions for their ages, eight years ago

Eight years ago, their ages were $x-8$ and $y-8$

According to the given condition,

$\frac{x-8}{y-8}=\frac{7}{13}$

$13x-104=$$7y-56$

$13x-7y=48\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots ..\left(2\right)$

Step2: Graphical Solution

$y=\frac{7x}{5}$ (from (1))

$x$	$5$	$0$	$-5$
$y$	$7$	$0$	$-7$

$y$=$\frac{13x-48}{7}$ (from (2))

$x$	$15$	$1$	$\frac{48}{13}=3.6\left(approx\right)$
$y$	$21$	$-5$	$0$

)

From the graph ,we can see that the lines intersect at the point(15,21)

Conclusion:

Hence the age of first girl= 15 years and the age of second girl=21years