To solve the problem where the sum of two numbers is 20 and their difference is 4, let's call these two numbers [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
We have two pieces of information:
1. The sum of the numbers: [tex]\( x + y = 20 \)[/tex]
2. The difference of the numbers: [tex]\( x - y = 4 \)[/tex]
We can set up these two equations:
[tex]\[
1. \ x + y = 20
\][/tex]
[tex]\[
2. \ x - y = 4
\][/tex]
### Step 1: Solve the System of Equations
We can solve these equations using the method of elimination or substitution. Here, elimination is straightforward:
Add the two equations:
[tex]\[ (x + y) + (x - y) = 20 + 4 \][/tex]
[tex]\[ x + y + x - y = 24 \][/tex]
[tex]\[ 2x = 24 \][/tex]
[tex]\[ x = 12 \][/tex]
Now substitute [tex]\( x = 12 \)[/tex] into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[ x + y = 20 \][/tex]
[tex]\[ 12 + y = 20 \][/tex]
[tex]\[ y = 20 - 12 \][/tex]
[tex]\[ y = 8 \][/tex]
### Conclusion:
The two numbers are [tex]\( 12 \)[/tex] and [tex]\( 8 \)[/tex].
Therefore, the correct answer is: (a) 12 and 8.
