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If
x and
y vary directly and
y is 24 when
x is 6 , find
y when
x is 3 .
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $24$ when $x$ is $6$ , find $y$ when $x$ is $3$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

vary directly and

y

is

24

when

x

is

6

, find

y

when

x

is

3

.

\newline

Answer:

y=

Write Equation: Write the equation that represents the direct variation between $x$ and $y$ . Since $y$ varies directly with $x$ , the equation can be written as $y = kx$ , where $k$ is the constant of variation.
Find Constant: Use the given values to find the constant of variation $k$ . We know that $y = 24$ when $x = 6$ . Substitute these values into the direct variation equation to find $k$ . $24 = k \times 6$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $6$ to isolate k. $\newline$ $k = \frac{24}{6}$ $\newline$ $k = 4$
Write with $k$ : Write the direct variation equation with the found value of $k$ . Now that we know $k = 4$ , the direct variation equation is $y = 4x$ .
Find $y$ : Find $y$ when $x = 3$ using the direct variation equation. $\newline$ Substitute $x = 3$ into the equation $y = 4x$ to find $y$ . $\newline$ $y = 4 \times 3$ $\newline$ $y = 12$

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