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The problem shown in the image states:

**Problem**:
The ratio of two numbers is 3:7. When 5 is subtracted from each of those numbers, the new ratio is 1:3. What is the smaller of those two numbers before 5 is subtracted?

Let the two numbers be \(3x\) and \(7x\) (since their ratio is 3:7).

### Step 1: Express the new ratio after subtraction
After subtracting 5 from each of the two numbers, the ratio becomes 1:3, so:
\[
\frac{3x - 5}{7x - 5} = \frac{1}{3}
\]

### Step 2: Set up the equation
Cross-multiply to eliminate the fraction:
\[
3(3x - 5) = 1(7x - 5)
\]

Expanding both sides:
\[
9x - 15 = 7x - 5
\]

### Step 3: Solve for \(x\)
Move all terms involving \(x\) to one side:
\[
9x - 7x = -5 + 15
\]
\[
2x = 10
\]
\[
x = 5
\]

### Step 4: Calculate the numbers
The two numbers are \(3x = 3(5) = 15\) and \(7x = 7(5) = 35\).

Thus, the smaller of the two numbers before 5 is subtracted is **15**.

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Do you want further explanation or have any questions about this solution? 

Here are 5 additional related questions to explore:

1. If the ratio of two numbers is 5:9, and subtracting 4 from both makes the ratio 1:2, what are the original numbers?
2. How do ratios change if you subtract a constant from both terms of the ratio?
3. Can you solve a similar problem where the ratio of two numbers is 4:5, and subtracting 3 from both gives a ratio of 2:3?
4. What happens to a ratio when the same constant is added to both terms?
5. How would the solution change if instead of subtracting 5, we added 5 to both numbers?

**Tip**: Whenever working with ratios, setting the terms as multiples of a variable (like \(3x\) and \(7x\)) helps simplify the algebra involved in solving such problems.

The ratio of two numbers is 3:7. When 5 is subtracted from each of those numbers, the new ratio is 1:3. What is the smaller of those two numbers before 5 is subtracted?

Explore how to solve ratio problems by subtracting a constant from both terms, using a specific example where the ratio 3:7 changes to 1:3 after subtraction. This problem is well-suited for middle school students studying algebra.

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