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]
4. Simplify the ratio:
[tex]\[
\frac{24}{20} = \frac{24 \div 4}{20 \div 4} = \frac{6}{5}
\][/tex]
Therefore, the ratio of the two numbers is [tex]\( 6:5 \)[/tex].
Answer:
The ratio of the two numbers is [tex]\( 6:5 \)[/tex], which corresponds to option [tex]\( c. 6:5 \)[/tex].
