College

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 :

Certainly! Let's solve the problem step-by-step.

The problem states that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means we can express the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] using the equation:

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

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

We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use this information to find the value of [tex]\( k \)[/tex]:

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

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

[tex]\[ k = \frac{7}{28} = \frac{1}{4} \][/tex]

Now that we know [tex]\( k = \frac{1}{4} \)[/tex], let's find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex].

Using the equation [tex]\( y = kx \)[/tex] again, substitute [tex]\( y = 3 \)[/tex] and [tex]\( k = \frac{1}{4} \)[/tex] into the equation:

[tex]\[ 3 = \frac{1}{4} \times x \][/tex]

To solve for [tex]\( x \)[/tex], multiply both sides by 4 to get rid of the fraction:

[tex]\[ x = 3 \times 4 = 12 \][/tex]

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

Among the answer choices provided, option "c" corresponds to this result. So, the correct answer is:

c. 12