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If
x and
y vary directly and
y is 25 when
x is 5 , find
y when
x is 10 .
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $25$ when $x$ is $5$ , find $y$ when $x$ is $10$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

vary directly and

y

is

25

when

x

is

5

, find

y

when

x

is

10

.

\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 $y = 25$ when $x = 5$ . Substitute these values into the direct variation equation to find $k$ . $25 = k \times 5$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $5$ to isolate k. $\newline$ $\frac{25}{5} = k$ $\newline$ $k = 5$
Write with $k$ : Write the direct variation equation with the found value of $k$ . Now that we know $k = 5$ , the direct variation equation is $y = 5x$ .
Find $y$ : Use the direct variation equation to find $y$ when $x = 10$ . Substitute $x = 10$ into the equation $y = 5x$ . $y = 5 \times 10$ $y = 50$

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