The sum of two numbers is 150. The ratio of the same two numbers is 3:2. Find the bigger number.

The two numbers are x and y; therefore we can suggest this system of equations:

x+y=150

x/y=3/2

We can solve this system of equations by substitution method.

x/y=3/2 ⇒x=3y/2

(3y/2) + y=150

3y/2 + y=150

lowest common multiple=2

3y+2y=300

5y=300

y=300/5

y=60

x=3y/2

x = (3*60) / 2=180/2=90

Answer: the bigger number is 90