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If
x and
y vary directly and
y is 7 when
x is 14 , find
y when
x is 8 .
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $7$ when $x$ is $14$ , find $y$ when $x$ is $8$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

vary directly and

y

is

7

when

x

is

14

, find

y

when

x

is

8

.

\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 $y = 7$ when $x = 14$ . Substitute these values into the direct variation equation to find $k$ . $7 = k \times 14$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $14$ to isolate $k$ . $\newline$ $k = \frac{7}{14}$ $\newline$ $k = 0.5$
Write with $k$ : Write the direct variation equation with the found value of $k$ . Now that we have found $k$ to be $0.5$ , the direct variation equation is $y = 0.5x$ .
Find $y$ : Use the direct variation equation to find $y$ when $x$ is $8$ . Substitute $x = 8$ into the equation $y = 0.5x$ to find $y$ . $y = 0.5 \times 8$ $y = 4$

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