To solve the problem, we need to find two numbers whose sum is 44 and whose difference is 4. We will then calculate the ratio of these two numbers.
Step-by-Step Solution:
1. Set up the equations: Let the first number be [tex]\( x \)[/tex] and the second number be [tex]\( y \)[/tex].
From the problem statement, we have two key pieces of information: [tex]\[
x + y = 44 \quad \text{(Equation 1)}
\][/tex] [tex]\[
x - y = 4 \quad \text{(Equation 2)}
\][/tex]
2. Solve the system of equations: We can solve these equations simultaneously to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
- Add the two equations: [tex]\[
(x + y) + (x - y) = 44 + 4
\][/tex] Simplifying this, [tex]\[
2x = 48
\][/tex] [tex]\[
x = 24
\][/tex]
- Substitute [tex]\( x \)[/tex] back into Equation 1: [tex]\[
24 + y = 44
\][/tex] Solving for [tex]\( y \)[/tex], [tex]\[
y = 44 - 24
\][/tex] [tex]\[
y = 20
\][/tex]
So, the two numbers are [tex]\( x = 24 \)[/tex] and [tex]\( y = 20 \)[/tex].
3. Calculate the ratio of the two numbers: The ratio of the first number to the second number is: [tex]\[
\frac{x}{y} = \frac{24}{20}
\][/tex]
