Answer :
To solve this problem, we'll use the concept of direct variation. When a variable [tex]\( y \)[/tex] varies directly as another variable [tex]\( x \)[/tex], it means that:
[tex]\[
y = k \cdot x
\][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
### Step 1: Find the Constant of Variation
You're given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. So, you can substitute these values into the equation to find [tex]\( k \)[/tex]:
[tex]\[
7 = k \cdot 28
\][/tex]
Divide both sides by 28 to solve for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{7}{28} = 0.25
\][/tex]
### Step 2: Use the Constant to Find [tex]\( x \)[/tex] When [tex]\( y = 3 \)[/tex]
Now, you need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]. Substitute [tex]\( y = 3 \)[/tex] and the value of [tex]\( k \)[/tex] into the direct variation equation:
[tex]\[
3 = 0.25 \cdot x
\][/tex]
To find [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 12.
The correct answer is: c. 12
[tex]\[
y = k \cdot x
\][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
### Step 1: Find the Constant of Variation
You're given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. So, you can substitute these values into the equation to find [tex]\( k \)[/tex]:
[tex]\[
7 = k \cdot 28
\][/tex]
Divide both sides by 28 to solve for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{7}{28} = 0.25
\][/tex]
### Step 2: Use the Constant to Find [tex]\( x \)[/tex] When [tex]\( y = 3 \)[/tex]
Now, you need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]. Substitute [tex]\( y = 3 \)[/tex] and the value of [tex]\( k \)[/tex] into the direct variation equation:
[tex]\[
3 = 0.25 \cdot x
\][/tex]
To find [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 12.
The correct answer is: c. 12
