Answer:
The numbers are : 15 and 25
solution,
Let the number be X and y
[tex] \frac{x}{y} = \frac{3}{5} \\ or \: x \times 5 = 3 \times y \\ or \: 5x = 3y \\ or \: x = \frac{3y}{5} ............ > equation \: i \\ [/tex]
If 5 is added to each number,
[tex] \frac{x + 5}{y + 5} = \frac{2}{3} \\ or \: 3(x + 5) = 2(y + 5) \\ or \: 3x + 15 = 2y + 10 \\ or \: 3x - 2y = - 5[/tex]
putting the value of X
[tex]3 \times \frac{3y}{5} - 2y = - 5 \\ or \: \frac{9y}{5} - 2y = - 5 \\ or \: \frac{9y - 2y \times 5}{5} = - 5 \\ or \: \frac{9y - 10y}{5} = - 5 \\ or - y = - 5 \times 5 \\ or \: - y = - 25 \\ y = 25[/tex]
Replacing the value of y in equation (i)
[tex]x = \frac{3y}{5} \\ x = \frac{3 \times 25}{5} \\ x = \frac{75}{5} \\ x = 15[/tex]
The value of X is 15.
The value of y is 25.
Hence,the two numbers are 15 and 25.
Hope this helps...
Good luck on your assignment..
