The difference between the two numbers is 48. The ratio of the two numbers is 7:3. What is the smaller number 

Let the two numbers be \( x \) and \( y \), where \( x \) is the larger number and \( y \) is the smaller number.

From the problem, we have two pieces of information:
1. The difference between the two numbers is 48:
   \[
   x - y = 48
   \]
2. The ratio of the two numbers is 7:3:
   \[
   \frac{x}{y} = \frac{7}{3}
   \]
   
We can solve this step-by-step.

### Step 1: Express \( x \) in terms of \( y \)
From the ratio \( \frac{x}{y} = \frac{7}{3} \), we can cross-multiply:
\[
x = \frac{7}{3}y
\]

### Step 2: Substitute \( x \) into the difference equation
Now, substitute \( x = \frac{7}{3}y \) into the equation \( x - y = 48 \):
\[
\frac{7}{3}y - y = 48
\]

### Step 3: Solve for \( y \)
To simplify the left side, write \( y \) as \( \frac{3}{3}y \):
\[
\frac{7}{3}y - \frac{3}{3}y = 48
\]
\[
\frac{4}{3}y = 48
\]

Multiply both sides by 3 to eliminate the fraction:
\[
4y = 144
\]

Now, divide by 4:
\[
y = 36
\]

### Step 4: Conclusion
The smaller number is \( \boxed{36} \).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to consider:
1. How do you solve ratio problems when more than two numbers are involved?
2. Can you verify the solution by checking both the ratio and difference conditions?
3. How would the problem change if the ratio were reversed (3:7)?
4. What happens if the difference is halved while keeping the same ratio?
5. How can this approach be applied to problems involving percentages instead of ratios?

**Tip:** Always double-check your solution by substituting it back into the original equations to ensure accuracy.

The difference between the two numbers is 48. The ratio of the two numbers is 7:3. What is the smaller number?

Discover how to solve for the smaller number when the ratio of two numbers is 7:3 and their difference is 48. This problem applies algebraic concepts like solving linear equations and working with ratios. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation