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Answer :
Certainly! Let's solve the problem step-by-step.
The problem states that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means we can express the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] using the equation:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use this information to find the value of [tex]\( k \)[/tex]:
[tex]\[ 7 = k \times 28 \][/tex]
To solve for [tex]\( k \)[/tex], divide both sides by 28:
[tex]\[ k = \frac{7}{28} = \frac{1}{4} \][/tex]
Now that we know [tex]\( k = \frac{1}{4} \)[/tex], let's find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex].
Using the equation [tex]\( y = kx \)[/tex] again, substitute [tex]\( y = 3 \)[/tex] and [tex]\( k = \frac{1}{4} \)[/tex] into the equation:
[tex]\[ 3 = \frac{1}{4} \times x \][/tex]
To solve for [tex]\( x \)[/tex], multiply both sides by 4 to get rid of the fraction:
[tex]\[ x = 3 \times 4 = 12 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex].
Among the answer choices provided, option "c" corresponds to this result. So, the correct answer is:
c. 12
The problem states that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means we can express the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] using the equation:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
We are given that [tex]\( y = 7 \)[/tex] when [tex]\( x = 28 \)[/tex]. We can use this information to find the value of [tex]\( k \)[/tex]:
[tex]\[ 7 = k \times 28 \][/tex]
To solve for [tex]\( k \)[/tex], divide both sides by 28:
[tex]\[ k = \frac{7}{28} = \frac{1}{4} \][/tex]
Now that we know [tex]\( k = \frac{1}{4} \)[/tex], let's find the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex].
Using the equation [tex]\( y = kx \)[/tex] again, substitute [tex]\( y = 3 \)[/tex] and [tex]\( k = \frac{1}{4} \)[/tex] into the equation:
[tex]\[ 3 = \frac{1}{4} \times x \][/tex]
To solve for [tex]\( x \)[/tex], multiply both sides by 4 to get rid of the fraction:
[tex]\[ x = 3 \times 4 = 12 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\( 12 \)[/tex].
Among the answer choices provided, option "c" corresponds to this result. So, the correct answer is:
c. 12
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