Answer :
To solve the problem where [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], we start by understanding that the relationship can be written as:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is a constant.
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. Substituting these values into the equation, we get:
[tex]\[ 7 = k \cdot 28 \][/tex]
To find the value of [tex]\( k \)[/tex], we solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{7}{28} = 0.25 \][/tex]
Now, we need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] using the same relationship [tex]\( y = kx \)[/tex]. We substitute [tex]\( y = 3 \)[/tex] into the equation:
[tex]\[ 3 = 0.25 \cdot x \][/tex]
To find [tex]\( x \)[/tex], we solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{0.25} = 12 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex].
The correct answer is:
c. 12
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is a constant.
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. Substituting these values into the equation, we get:
[tex]\[ 7 = k \cdot 28 \][/tex]
To find the value of [tex]\( k \)[/tex], we solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{7}{28} = 0.25 \][/tex]
Now, we need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] using the same relationship [tex]\( y = kx \)[/tex]. We substitute [tex]\( y = 3 \)[/tex] into the equation:
[tex]\[ 3 = 0.25 \cdot x \][/tex]
To find [tex]\( x \)[/tex], we solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{0.25} = 12 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex].
The correct answer is:
c. 12
