If y varies directly with x and y=20 when x=5, find y when x=3.
Write and solve a direct variation equation to find the answer.If y varies directly with x and y=20 when x=5, find y when x=3.
Write and solve a direct variation equation to find the answer.

In a direct variation, \( y \) varies directly with \( x \), meaning the relationship between \( y \) and \( x \) can be expressed as:

\[
y = kx
\]

where \( k \) is the constant of variation.

### Step 1: Find the constant of variation \( k \)
We are given that \( y = 20 \) when \( x = 5 \). Using this information, we substitute these values into the direct variation equation to find \( k \):

\[
20 = k(5)
\]

Solving for \( k \):

\[
k = \frac{20}{5} = 4
\]

### Step 2: Use the constant \( k \) to find \( y \) when \( x = 3 \)
Now that we know \( k = 4 \), we substitute this value into the direct variation equation and solve for \( y \) when \( x = 3 \):

\[
y = 4(3) = 12
\]

### Final Answer:
When \( x = 3 \), \( y = 12 \).

---

Would you like more details or further clarification on any step? Here are five related questions for practice:

1. If \( y \) varies directly with \( x \) and \( y = 15 \) when \( x = 3 \), what is \( y \) when \( x = 7 \)?
2. How do you know if two variables vary directly?
3. Find the constant of variation if \( y = 30 \) when \( x = 10 \).
4. If \( y = 2x \), what is \( y \) when \( x = 8 \)?
5. What happens to \( y \) as \( x \) increases in a direct variation?

**Tip:** In direct variation problems, always find the constant first, then use it to solve for unknown values.

If y varies directly with x and y = 20 when x = 5, find y when x = 3. Write and solve a direct variation equation to find the answer.

Learn how to solve a direct variation problem where y = 20 when x = 5. This problem demonstrates how to find the constant of variation and solve for y when x = 3. Suitable for middle school students in Grades 6-8.

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