Answer :
Sure! Let's solve the problem step-by-step.
We are told that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means there is a constant [tex]\( k \)[/tex] such that [tex]\( y = kx \)[/tex].
1. Find the constant of variation [tex]\( k \)[/tex]:
We know from the problem that when [tex]\( y = 7 \)[/tex], [tex]\( x = 28 \)[/tex]. Using the direct variation equation [tex]\( y = kx \)[/tex], we can substitute the known values:
[tex]\[
7 = k \times 28
\][/tex]
Solving for [tex]\( k \)[/tex], we divide both sides by 28:
[tex]\[
k = \frac{7}{28} = \frac{1}{4} = 0.25
\][/tex]
2. Use [tex]\( k \)[/tex] to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
Now that we know [tex]\( k = 0.25 \)[/tex], we use the direct variation equation to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
[tex]\[
3 = 0.25 \times x
\][/tex]
Solving for [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\(\boxed{12}\)[/tex]. So, the correct answer is option C.
We are told that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means there is a constant [tex]\( k \)[/tex] such that [tex]\( y = kx \)[/tex].
1. Find the constant of variation [tex]\( k \)[/tex]:
We know from the problem that when [tex]\( y = 7 \)[/tex], [tex]\( x = 28 \)[/tex]. Using the direct variation equation [tex]\( y = kx \)[/tex], we can substitute the known values:
[tex]\[
7 = k \times 28
\][/tex]
Solving for [tex]\( k \)[/tex], we divide both sides by 28:
[tex]\[
k = \frac{7}{28} = \frac{1}{4} = 0.25
\][/tex]
2. Use [tex]\( k \)[/tex] to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
Now that we know [tex]\( k = 0.25 \)[/tex], we use the direct variation equation to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
[tex]\[
3 = 0.25 \times x
\][/tex]
Solving for [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\(\boxed{12}\)[/tex]. So, the correct answer is option C.
