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Two numbers are in the ratio of 3:2 and their difference is 52. Find the numbers.
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.
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