Question

Two numbers are in the ratio of 4:7 the sum of three quarters of smaller number is 1/5 of largest number is 22 . Find the number

Answer 1

   $\bold{Answer:}$

   $\boxed{\text{20 and 35}}$

   $\bold{Step-by-step}$ $\bold{explaination:}$

   $\text{It is given that: Two numbers are in the ratio 4:7}$

                             $\text{Sum of three quarters of smaller number and } \frac{1}{5} \\\text{ of largest number is 22 }$

   $\text{Let the common factor of the ratio be }x$

⇒ $\text{The numbers are } 4x \text{ and } 7x$

⇒ $\frac{3}{4}(4x) + \frac{1}{5}(7x) = 22$

⇒ $3x + \frac{7x}{5} = 22$

⇒ $\frac{15x + 7x}{5} = 22$

⇒ $22x = 5(22)$

⇒ $x = 5$

∴ $\text{The numbers are: }4x= 4(5) = 20$

                                 $7x = 7(5) = 35$