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The value of
y varies directly with
x, and when
x=(1)/(4),y=25. What is the value of
y when
x is
2(1)/(3) ?
A.
233(1)/(3)
B.
9(1)/(3)
C.
14(1)/(2)
D.
213(1)/(4)

$3$ . The value of $y$ varies directly with $x$ , and when $x=\frac{1}{4}, y=25$ . What is the value of $y$ when $x$ is $2 \frac{1}{3}$ ? $\newline$ A. $233 \frac{1}{3}$ $\newline$ B. $9 \frac{1}{3}$ $\newline$ C. $14 \frac{1}{2}$ $\newline$ D. $213 \frac{1}{4}$

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Multiplication with rational exponents

Full solution

Q.

3

. The value of

y

varies directly with

x

, and when

x=\frac{1}{4}, y=25

. What is the value of

y

when

x

is

2 \frac{1}{3}

?

\newline

A.

233 \frac{1}{3}

\newline

B.

9 \frac{1}{3}

\newline

C.

14 \frac{1}{2}

\newline

D.

213 \frac{1}{4}

Identify Relationship: Identify the direct variation relationship between $y$ and $x$ . Given $y = 25$ when $x = \frac{1}{4}$ , find the constant of variation $k$ . Use the formula $y = kx$ . $\newline$ Calculation: $25 = k \times \left(\frac{1}{4}\right)$ $\newline$ Solving for $k$ gives $k = 25 \times 4 = 100$ .
Find Constant of Variation: Use the constant of variation $k$ to find $y$ when $x = \frac{2(1)}{3}$ . Convert the mixed number to an improper fraction. $\newline$ Calculation: $2\left(\frac{1}{3}\right) = \frac{7}{3}$ . $\newline$ Now, $y = 100 \times \left(\frac{7}{3}\right) = \frac{700}{3} = 233\left(\frac{1}{3}\right)$ .

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