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 :

Sure! Let's solve the problem step-by-step:

1. Understanding Direct Variation:
- 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]\( y = kx \)[/tex]. This [tex]\( k \)[/tex] is called the constant of variation.

2. Given Information:
- We know that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. This helps us find the constant [tex]\( k \)[/tex].

3. Find the Constant [tex]\( k \)[/tex]:
[tex]\[
y = kx \quad \Rightarrow \quad 7 = k \times 28
\][/tex]
[tex]\[
k = \frac{7}{28}
\][/tex]
[tex]\[
k = 0.25
\][/tex]

4. Use the Constant to Find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
- We now know [tex]\( y = 3 \)[/tex] and we need to find the corresponding [tex]\( x \)[/tex].
[tex]\[
y = kx \quad \Rightarrow \quad 3 = 0.25 \times x
\][/tex]
[tex]\[
x = \frac{3}{0.25}
\][/tex]
[tex]\[
x = 12
\][/tex]

5. Conclusion:
- The value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( \boxed{12} \)[/tex].

Therefore, the correct answer is option c. 12.

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