If y varies directly as x and y=12, where x=c, what is y in terms of c when x=8`?

Options

A. `(2c)/(3)`
B. `(3)/(2c)`
C. `20c`
D. `(96)/(c)`

Answer

To solve the problem, we need to follow these steps:

### Step 1: Understand the relationship
Since \( y \) varies directly as \( x \), we can express this relationship mathematically as:
\[ y = kx \]
where \( k \) is a constant of proportionality.

### Step 2: Find the constant \( k \)
We are given that \( y = 12 \) when \( x = c \). Substituting these values into the equation gives:
\[ 12 = kc \]
From this, we can express \( k \) as:
\[ k = \frac{12}{c} \]

### Step 3: Set up the equation for \( y \) when \( x = 8 \)
Now we want to find \( y \) when \( x = 8 \). Using the direct variation formula:
\[ y = kx \]
Substituting \( k \) from step 2 and \( x = 8 \):
\[ y = \left(\frac{12}{c}\right) \cdot 8 \]

### Step 4: Simplify the expression
Now simplify the equation:
\[ y = \frac{12 \cdot 8}{c} = \frac{96}{c} \]

### Conclusion
Thus, when \( x = 8 \), \( y \) in terms of \( c \) is:
\[ y = \frac{96}{c} \]

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