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Answer :
To solve this problem, we need to understand what it means for one variable to vary directly with another. When we say that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], it means there is a constant [tex]\( k \)[/tex] such that [tex]\( y = k \cdot x \)[/tex].
Let's go through the steps to find the solution:
1. Determine the constant of variation [tex]\( k \)[/tex]:
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use this information to find the constant [tex]\( k \)[/tex].
[tex]\[
y = k \cdot x \implies 7 = k \cdot 28
\][/tex]
Solving for [tex]\( k \)[/tex], we have:
[tex]\[
k = \frac{7}{28} = 0.25
\][/tex]
2. Find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
Now that we know [tex]\( k = 0.25 \)[/tex], we use the same direct variation equation to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
[tex]\[
y = k \cdot x \implies 3 = 0.25 \cdot x
\][/tex]
Solving for [tex]\( x \)[/tex], we get:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is 12. Therefore, the correct answer is c. 12.
Let's go through the steps to find the solution:
1. Determine the constant of variation [tex]\( k \)[/tex]:
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use this information to find the constant [tex]\( k \)[/tex].
[tex]\[
y = k \cdot x \implies 7 = k \cdot 28
\][/tex]
Solving for [tex]\( k \)[/tex], we have:
[tex]\[
k = \frac{7}{28} = 0.25
\][/tex]
2. Find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
Now that we know [tex]\( k = 0.25 \)[/tex], we use the same direct variation equation to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
[tex]\[
y = k \cdot x \implies 3 = 0.25 \cdot x
\][/tex]
Solving for [tex]\( x \)[/tex], we get:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is 12. Therefore, the correct answer is c. 12.
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