Question

Two numbers are in the ratio $4:7$. If thrice the larger be added to twice the smaller, the sum is $59$. Find the numbers.

Answer 1

Let the smaller number be $x$ and the larger number be $y$.

According to the question,

$\frac{x}{y}=\frac{4}{7}$

$\Rightarrow 7x-4y=0$...(1)

and, $3y+2x=59$...(2)

Multiplying equation no. (1) by $3$ and (2) by $4$ and adding them, we get,

$\Rightarrow 21x-12y+12y+8x=0+236$

$\Rightarrow 29x=236$

$\Rightarrow x=\frac{236}{29}$

From (i)

$\Rightarrow 7\left(\frac{236}{29}\right)=4y$

$\Rightarrow y=\frac{413}{29}$

Hence, the number are $\frac{236}{29}$ and $\frac{413}{29}$