To find the two numbers, we can set up two equations based on the given conditions:
1. The sum of the two numbers is 90.
2. The difference of the two numbers is 12.
Let's call the two numbers [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
From the conditions, we have:
1. [tex]\(x + y = 90\)[/tex]
2. [tex]\(x - y = 12\)[/tex]
We can solve these equations step-by-step:
Step 1: Add the two equations
When we add the two equations, we get:
[tex]\[
(x + y) + (x - y) = 90 + 12
\][/tex]
Simplify the left side of the equation:
[tex]\[
2x = 102
\][/tex]
Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{102}{2} = 51
\][/tex]
Step 2: Substitute the value of [tex]\(x\)[/tex] back into one of the original equations
We can use the first equation [tex]\(x + y = 90\)[/tex]:
[tex]\[
51 + y = 90
\][/tex]
Subtract 51 from both sides to solve for [tex]\(y\)[/tex]:
[tex]\[
y = 90 - 51 = 39
\][/tex]
So, the two numbers are 51 and 39.
Therefore, the correct option is:
- 39 and 51
