x, y - the numbers
The sum of two numbers is 150.
[tex]x+y=150 \ \ \ |-y \\ x=150-y[/tex]
The ratio of the two numbers is 3:2.
[tex]\frac{x}{y}=\frac{3}{2} \ \ \ |\times y \\
x=\frac{3}{2}y[/tex]
Set both expressions equal to each other:
[tex]x=x \\
150-y=\frac{3}{2}y \ \ \ |+y \\
150=\frac{3}{2}y+y \\
150=\frac{3}{2}y+\frac{2}{2}y \\
150=\frac{5}{2}y \ \ \ |\times \frac{2}{5} \\
150 \times \frac{2}{5}=y \\
30 \times 2=y \\
y=60 \\ \\
x=150-y=150-60=90[/tex]
The numbers are 60 and 90.
The bigger number is 90.
