Question

A positive number is 7 times another number. If 15 is added to both the numbers,
then one of the new number becomes 5/2 times the other new number. What are the
numbers?​

Answer 1

Given :

• A positive number is 7 times another number.
• If 15 is added to both the numbers , one of the new number becomes 5/2 times the other number.

To Find :

• Two positive numbers.

Solution :

$\longmapsto\tt{Let\:first\:positive\:no.=x}$

As Given that another number is 7 times of first Number. So ,

$\longmapsto\tt{Second\:No.=7x}$

A.T.Q :

• If 15 is added to both the numbers , one of the new number becomes 5/2 times the other number.

$\longmapsto\tt{\dfrac{5}{2}\times\bigg({x+\dfrac{15}{1}}\bigg)=7x+15}$

$\longmapsto\tt{\dfrac{5x}{2}+\dfrac{75}{2}=7x+15}$

$\longmapsto\tt{\dfrac{5x}{2}-\dfrac{7x}{1}=\dfrac{15}{1}-\dfrac{75}{2}}$

$\longmapsto\tt{\dfrac{5x-14}{2}=\dfrac{30-75}{2}}$

$\longmapsto\tt{\dfrac{-9x}{{\cancel{2}}}=\dfrac{-45}{{\cancel{2}}}}$

$\longmapsto\tt{x=\cancel\dfrac{-45}{-9}}$

$\longmapsto\tt\bold{x=5}$

Value of x is 5...

Therefore :

$\longmapsto\tt\bold{First\:Positive\:No.=5}$

$\longmapsto\tt{Second\:Positive\:No.=7(5)}$

$\longmapsto\tt\bold{35}$