Two number are in the ratio 3:7 if 8 is added both the numbers, their ration become 5:9 the number are 

Let the two numbers be \(3x\) and \(7x\) according to the given ratio \(3:7\).

When 8 is added to both numbers, their new values become:
- \(3x + 8\)
- \(7x + 8\)

According to the problem, the new ratio becomes \(5:9\). Therefore, we can set up the equation:

\[
\frac{3x + 8}{7x + 8} = \frac{5}{9}
\]

Now, cross-multiply to solve for \(x\):

\[
9(3x + 8) = 5(7x + 8)
\]

Expanding both sides:

\[
27x + 72 = 35x + 40
\]

Now, isolate \(x\) by moving all \(x\)-terms to one side and constants to the other:

\[
72 - 40 = 35x - 27x
\]

\[
32 = 8x
\]

\[
x = 4
\]

Now that we have \(x = 4\), we can substitute it back to find the numbers:

\[
3x = 3 \times 4 = 12
\]
\[
7x = 7 \times 4 = 28
\]

So, the two numbers are **12 and 28**.

---

Would you like more details on the steps? 

Here are some questions to further explore similar concepts:
1. What if the ratio change involved subtraction instead of addition?
2. How would the solution differ if the ratio change was given as \(5:8\) instead of \(5:9\)?
3. Can ratios be used to compare more than two quantities in similar problems?
4. What if the initial ratio was fractional or in decimal form?
5. How does this problem change if we multiply both numbers instead of adding?

**Tip:** Cross-multiplying is a common way to solve proportion problems by eliminating fractions.

Two numbers are in the ratio 3:7. If 8 is added to both numbers, their ratio becomes 5:9. Find the numbers.

Learn how to find two numbers in a 3:7 ratio, where adding 8 to each results in a 5:9 ratio. This problem explores key algebra concepts, such as setting up proportions and cross-multiplication. Ideal for Grades 7-9 students.

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