Let's solve the problem step by step.
We're given two pieces of information about two numbers, which we'll call \( x \) and \( y \):
1. \( x + y = 49 \)
2. \( x - y = 5 \)
To find the values of \( x \) and \( y \), we can use the method of solving simultaneous equations.
First, let's add the two equations:
[tex]\[
(x + y) + (x - y) = 49 + 5
\][/tex]
This simplifies to:
[tex]\[
2x = 54
\][/tex]
Now, solve for \( x \):
[tex]\[
x = \frac{54}{2} = 27
\][/tex]
Next, substitute \( x = 27 \) back into the first equation to find \( y \):
[tex]\[
27 + y = 49
\][/tex]
Now, solve for \( y \):
[tex]\[
y = 49 - 27 = 22
\][/tex]
So, the two numbers are:
[tex]\[
(27, 22)
\][/tex]
Therefore, the numbers are 27 and 22.
