Let the two numbers be x and y
since the ratio the two numbers is 4:3,
we can write,
[tex] \frac{x}{y} = \frac{4}{3} [/tex]
[tex]3x = 4y[/tex]
[tex]x = \frac{4}{3} y[/tex]
If 5 is subtracted from this ratio , the new ratio is 7:3. It can be written as,
[tex] \frac{x - 5}{y - 5} = \frac{7}{3} [/tex]
[tex]3(x - 5) = 7(y - 5)[/tex]
[tex]3x - 15 = 7y - 35[/tex]
[tex]put \: x = \frac{4}{3} y \: in \: \: 3x - 15 = 3y - 35,[/tex]
we get,
[tex]3( \frac{4}{3} y) - 15 = 7y - 35[/tex]
[tex] \frac{12y}{3} - 7y = - 35 + 15[/tex]
[tex] \frac{12y - 21y}{3} = - 20[/tex]
[tex] - 9y = - 60[/tex]
[tex]y = \frac{60}{9} [/tex]
[tex]y = \frac{20}{3} [/tex]
[tex]put \: y = \frac{60}{3 } \: \: \: in \: \: x = \frac{4}{3} y,[/tex]
we get,
[tex]x = \frac{4}{3} \times \frac{20}{3} [/tex]
[tex]x = \frac{80}{9} [/tex]
[tex]hence \: the \: numbers \: are \: \: \frac{60}{3 } \: and \: \: \frac{80}{3} [/tex]
