Answer :
To solve this problem, we're dealing with a situation where [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means that the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] can be expressed using a constant [tex]\( k \)[/tex], such that [tex]\( y = kx \)[/tex].
### Step 1: Find the Constant of Variation
First, we need to determine the constant [tex]\( k \)[/tex]. We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use these values to find [tex]\( k \)[/tex]:
[tex]\[
y = kx \\
7 = k \cdot 28
\][/tex]
To find [tex]\( k \)[/tex], divide both sides of the equation by 28:
[tex]\[
k = \frac{7}{28} = 0.25
\][/tex]
### Step 2: Use the Constant to Find the New Value of [tex]\( x \)[/tex]
Now, we need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]. We know that the same constant [tex]\( k = 0.25 \)[/tex] applies, so we have:
[tex]\[
y = kx \\
3 = 0.25 \cdot x
\][/tex]
To solve for [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
### Conclusion
The value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex]. Therefore, the correct answer is option c, 12.
### Step 1: Find the Constant of Variation
First, we need to determine the constant [tex]\( k \)[/tex]. We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use these values to find [tex]\( k \)[/tex]:
[tex]\[
y = kx \\
7 = k \cdot 28
\][/tex]
To find [tex]\( k \)[/tex], divide both sides of the equation by 28:
[tex]\[
k = \frac{7}{28} = 0.25
\][/tex]
### Step 2: Use the Constant to Find the New Value of [tex]\( x \)[/tex]
Now, we need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]. We know that the same constant [tex]\( k = 0.25 \)[/tex] applies, so we have:
[tex]\[
y = kx \\
3 = 0.25 \cdot x
\][/tex]
To solve for [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
### Conclusion
The value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex]. Therefore, the correct answer is option c, 12.
