Identify the variables and write a system of equations for the story problem.
Step 1, label variables.
x=larger number
y=smaller number
Step 2, Convert sentences into equations
The sum of 2 numbers is 33.
x + y = 33
The larger number (x) is 3 more than 2 times the smaller number (y)
x = 2y + 3
Step 3: Substitute second equation into first equation and solve for y.
(2y + 3) + y = 33
3y + 3 -3 = 33 -3
3y/3 = 30/3
y = 10
Step 4: Substitute solved value for y and solve for x
x = 2y + 3
x = 2(10) + 3
x = 20 + 3 = 23
Step 5: Check x+y=33, 23 + 10 = 33 Check.