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If
x and
y vary directly and
y is 4 when
x is 12 , find
y when
x is 15 .
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $4$ when $x$ is $12$ , find $y$ when $x$ is $15$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

vary directly and

y

is

4

when

x

is

12

, find

y

when

x

is

15

.

\newline

Answer:

y=

Establish Relationship: Establish the direct variation relationship. $\newline$ Since $y$ varies directly with $x$ , we can write the relationship as $y = kx$ , where $k$ is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation $k$ . We know that $y = 4$ when $x = 12$ . Substitute these values into the direct variation equation to find $k$ . $4 = k \times 12$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $12$ to isolate $k$ . $\newline$ $k = \frac{4}{12}$ $\newline$ $k = \frac{1}{3}$
Write Equation with $k$ : Write the direct variation equation with the found value of $k$ . Now that we know $k = \frac{1}{3}$ , the direct variation equation is $y = \left(\frac{1}{3}\right)x$ .
Find $y$ for $x=15$ : Use the direct variation equation to find $y$ when $x$ is $15$ . Substitute $x = 15$ into the equation $y = \frac{1}{3}x$ . $y = \frac{1}{3} \times 15$ $y = 5$

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