To find the two numbers, let’s denote them as x and y.
According to the problem, we have two equations:
- x + y = 40 (1)
- x – y = 10 (2)
Now, we can solve these equations step by step.
First, we can add both equations (1) and (2):
(x + y) + (x – y) = 40 + 10
This simplifies to:
2x = 50
Now, divide both sides by 2:
x = 25
Having found x, we can now substitute it back into one of the original equations to find y. Let’s use equation (1):
25 + y = 40
Subtract 25 from both sides:
y = 15
Therefore, the two numbers are 25 and 15.
In conclusion, the two numbers that satisfy both conditions—where their sum is 40 and their difference is 10—are 25 and 15.