High School

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 :

Sure! Let's work through this problem step-by-step.

We are told that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], which means the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] can be described by the equation:

[tex]\[ y = kx \][/tex]

where [tex]\( k \)[/tex] is the constant of variation.

We know from the problem that when [tex]\( y = 7 \)[/tex], [tex]\( x = 28 \)[/tex]. We can use this information to find the constant [tex]\( k \)[/tex]:

[tex]\[ 7 = k \times 28 \][/tex]

To solve for [tex]\( k \)[/tex], divide both sides by 28:

[tex]\[ k = \frac{7}{28} \][/tex]
[tex]\[ k = 0.25 \][/tex]

Now that we have [tex]\( k \)[/tex], we can use this constant to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex].

The equation becomes:

[tex]\[ 3 = 0.25 \times x \][/tex]

To solve for [tex]\( x \)[/tex], divide both sides by 0.25:

[tex]\[ x = \frac{3}{0.25} \][/tex]

[tex]\[ x = 12 \][/tex]

So, when [tex]\( y = 3 \)[/tex], the value of [tex]\( x \)[/tex] is 12.

Therefore, the correct answer is:
c. 12