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The problem presents two equivalent ratios:

\[
A : 8 : 5 = 9 : 24 : B
\]

We need to determine the values of \(A\) and \(B\).

### Step 1: Finding \(A\)
We can use the first two terms of both ratios to find \(A\). Since the ratios are equivalent:

\[
\frac{A}{9} = \frac{8}{24}
\]

Simplifying the fraction on the right side:

\[
\frac{8}{24} = \frac{1}{3}
\]

Now, solve for \(A\):

\[
\frac{A}{9} = \frac{1}{3}
\]

Multiply both sides by 9:

\[
A = 9 \times \frac{1}{3} = 3
\]

### Step 2: Finding \(B\)
Next, use the last terms of both ratios:

\[
\frac{5}{B} = \frac{9}{24}
\]

Simplify the fraction on the right side:

\[
\frac{9}{24} = \frac{3}{8}
\]

Now solve for \(B\):

\[
\frac{5}{B} = \frac{3}{8}
\]

Cross-multiply:

\[
5 \times 8 = 3 \times B
\]

\[
40 = 3B
\]

Now divide both sides by 3:

\[
B = \frac{40}{3} \approx 13.33
\]

### Final Answer:
- \(A = 3\)
- \(B = \frac{40}{3} \approx 13.33\)

Would you like any further clarification or details?

Here are some related questions you can explore:
1. How can you verify if two ratios are equivalent?
2. What happens when you cross-multiply in proportions?
3. Can you always simplify ratios before solving for unknowns?
4. How would this change if you had four terms instead of three?
5. How do equivalent ratios relate to fractions?

**Tip:** Always simplify ratios or fractions first to make calculations easier!

Work out the values of A and B in these equivalent ratios: A:8:5 = 9:24:B

Find the values of A and B in the equivalent ratios A:8:5 = 9:24:B. This problem covers key concepts like ratios, cross-multiplication, and solving for unknowns. Suitable for students in Grades 6-8.

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