The sum of two numbers is 50. Two times the smaller number exceeds the larger number by 31. Find the numbers.

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