Answer:
Set two equations:
- Number #1 = x
- Number #2 = y
[tex]\left \{ {{x+y=50} \atop {\frac{x}{y}=\frac{7}{11} }} \right.[/tex]
Rearrange one of the equations to find the value of a variable:
[tex]x+y=50\\x=50-y[/tex]
Substitute in that value into the other equation:
[tex]\frac{50-y}{y}=\frac{7}{11}[/tex]
Cross-multiply & solve for y:
[tex]7y=11(50-y) \\7y=550-11y\\7y+11y=550\\18y=550\\y=\frac{550}{18}=\frac{275}{9}[/tex]
Substitute in the value to the original equation to find x:
[tex]\frac{x}{\frac{275}{9}}=\frac{7}{11} \\\frac{9x}{275}=\frac{7}{11} \\9(11)x=275(7)\\99x=1925\\x=\frac{1925}{99} =\frac{175}{9}[/tex]
Therefore, the answer will be:
- x = [tex]\frac{175}{9}[/tex]
- y = [tex]\frac{275}{9}[/tex]
You can check your answers by:
[tex]\frac{175}{9} +\frac{275}{9} =\frac{450}{9} =50[/tex]
[tex]\frac{\frac{175}{9} }{\frac{275}{9} } =\frac{175}{9} *\frac{9}{275} =\frac{175}{275}=\frac{7}{11}[/tex]
