Answer: X = 78 and Y = 22.
Explanation:
Let's call the two numbers X and Y. We are given two pieces of information:
1. The sum of the two numbers is 100, so we can write this as an equation: X + Y = 100.
2. The difference between the two numbers is 56, which can also be written as an equation: X - Y = 56.
Now, you have a system of two equations with two variables:
1. X + Y = 100
2. X - Y = 56
You can solve this system of equations by adding the two equations together to eliminate the Y variable:
(X + Y) + (X - Y) = 100 + 56
This simplifies to:
2X = 156
Now, divide both sides by 2 to solve for X:
2X / 2 = 156 / 2
X = 78
Now that you know the value of X, you can substitute it into one of the original equations to find the value of Y. Let's use the first equation:
X + Y = 100
78 + Y = 100
Subtract 78 from both sides:
Y = 100 - 78
Y = 22
So, the two numbers are X = 78 and Y = 22.