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Suppose [tex]y[/tex] varies directly as [tex]x[/tex]. If [tex]y = 7[/tex] when [tex]x = 28[/tex], what is the value of [tex]x[/tex] when [tex]y = 3[/tex]?

A. 7
B. 9
C. 12
D. 16

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

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