Malone Mccarthy
04/10/2024 · Senior High School
\( \frac { 9 } { \square } = \frac { 6 } { 18 } = \frac { \square } { 9 } \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the equation \( \frac{9}{\square} = \frac{6}{18} = \frac{\square}{9} \), we first simplify the fraction \( \frac{6}{18} \).
\[
\frac{6}{18} = \frac{1}{3}
\]
Now we can set up the equations based on the equality:
1. \( \frac{9}{\square} = \frac{1}{3} \)
2. \( \frac{\square}{9} = \frac{1}{3} \)
### Solving the first equation:
From \( \frac{9}{\square} = \frac{1}{3} \), we can cross-multiply:
\[
9 \cdot 3 = 1 \cdot \square
\]
This simplifies to:
\[
27 = \square
\]
### Solving the second equation:
From \( \frac{\square}{9} = \frac{1}{3} \), we can also cross-multiply:
\[
\square \cdot 3 = 1 \cdot 9
\]
This simplifies to:
\[
3\square = 9
\]
Dividing both sides by 3 gives:
\[
\square = 3
\]
### Conclusion:
We have two different values for \( \square \) from the two equations. Let's check if they are consistent with the original equation.
1. If \( \square = 27 \):
- \( \frac{9}{27} = \frac{1}{3} \) (True)
- \( \frac{27}{9} = 3 \) (Not equal to \( \frac{1}{3} \))
2. If \( \square = 3 \):
- \( \frac{9}{3} = 3 \) (Not equal to \( \frac{1}{3} \))
- \( \frac{3}{9} = \frac{1}{3} \) (True)
Thus, the only consistent value for \( \square \) that satisfies both parts of the equation is:
\[
\boxed{27}
\]
Quick Answer
The value of \( \square \) is 27.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit