Certainly! Let's solve the problem step-by-step.
We are given two key pieces of information about two numbers:
1. Their sum is 20.
2. Their difference is 4.
Let's denote these two numbers as [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
From the given information, we can set up the following system of equations:
1. [tex]\( x + y = 20 \)[/tex]
2. [tex]\( x - y = 4 \)[/tex]
To find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we can solve these equations simultaneously.
Step 1: Add the two equations
[tex]\[ (x + y) + (x - y) = 20 + 4 \][/tex]
This simplifies to:
[tex]\[ x + y + x - y = 24 \][/tex]
[tex]\[ 2x = 24 \][/tex]
Step 2: Solve for [tex]\( x \)[/tex]
[tex]\[ x = \frac{24}{2} \][/tex]
[tex]\[ x = 12 \][/tex]
Step 3: Substitute the value of [tex]\( x \)[/tex] back into the first equation
[tex]\[ 12 + y = 20 \][/tex]
Step 4: Solve for [tex]\( y \)[/tex]
[tex]\[ y = 20 - 12 \][/tex]
[tex]\[ y = 8 \][/tex]
So, the two numbers are [tex]\( x = 12 \)[/tex] and [tex]\( y = 8 \)[/tex].
Therefore, the correct answer is:
(a) 12 and 8
