Certainly! Let's solve the problem of finding the two numbers that are in the ratio of 3:2 and have a difference of 52.
### Step-by-Step Solution:
1. Understanding the ratio:
- The ratio 3:2 means that if we denote the two numbers as [tex]\(3x\)[/tex] and [tex]\(2x\)[/tex], their ratio translates to [tex]\( \frac{3x}{2x} = \frac{3}{2} \)[/tex].
2. Given difference:
- The difference between the two numbers is given as 52.
3. Setting up the equation:
- We can express this relationship mathematically:
[tex]\[
3x - 2x = 52
\][/tex]
- Simplifying, we get:
[tex]\[
x = 52
\][/tex]
4. Calculating the two numbers:
- Now, we use the value of [tex]\( x \)[/tex] to find the two numbers:
- The first number is [tex]\( 3x \)[/tex]:
[tex]\[
3x = 3 \times 52 = 156
\][/tex]
- The second number is [tex]\( 2x \)[/tex]:
[tex]\[
2x = 2 \times 52 = 104
\][/tex]
### Conclusion:
- The two numbers that are in the ratio of 3:2 and have a difference of 52 are 156 and 104.
