Answer:
The smaller number is 23, the larger number is 27
Step-by-step explanation:
Let x represent the smaller number, and let y represent the larger number, we can set up two equations from the given information.
"The sum of two numbers is 50" becomes x + y = 50
and
"Two times the smaller number exceeds the larger number by 31" becomes
2x = y + 31 (twice the smaller number is 31 more than the larger number)
so we have
x + y = 50
2x = y + 31
We will use substitution method to solve this system of equations
Step 1: Solve the second equation for 'y'
2x - 31 = y (subtract 31 from both sides to isolate 'y'), this can be rewritten as
y = 2x - 31
now plug that into the first equation and solve...
x + (2x - 31) = 50 (y becomes 2x - 31)
x + 2x - 31 = 50
3x = 81
x = 27
Since x = 27, y = 23
