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
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
