Given that two numbers are in the ratio of 5:3 and their difference is 18, let's find these numbers step-by-step.
1. Define the relationship in terms of a variable:
Let's say the numbers are [tex]\( 5x \)[/tex] and [tex]\( 3x \)[/tex], where [tex]\( x \)[/tex] is the common multiplier.
2. Set up the equation based on the difference:
According to the problem, the difference between the two numbers is 18. Therefore,
[tex]\[
5x - 3x = 18
\][/tex]
3. Simplify the equation:
Simplifying the left-hand side, we get:
[tex]\[
2x = 18
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by 2 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{18}{2} = 9
\][/tex]
5. Calculate the numbers:
Now that we have [tex]\( x = 9 \)[/tex], we can find the actual numbers:
[tex]\[
\text{First number} = 5x = 5 \times 9 = 45
\][/tex]
[tex]\[
\text{Second number} = 3x = 3 \times 9 = 27
\][/tex]
So, the two numbers are 45 and 27.
