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If
x and
y vary directly and
y is 55 when
x is 11 , find
y when
x is 13.
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $55$ when $x$ is $11$ , find $y$ when $x$ is $13$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

vary directly and

y

is

55

when

x

is

11

, find

y

when

x

is

13

.

\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 $y = 55$ when $x = 11$ . Substituting these values into the direct variation equation gives us $55 = k \times 11$ .
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $11$ to isolate k. $\newline$ $k = \frac{55}{11}$ $\newline$ $k = 5$
Write Equation 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 $y$ for $x=13$ : Find $y$ when $x = 13$ using the direct variation equation. $\newline$ Substitute $x = 13$ into the equation $y = 5x$ . $\newline$ $y = 5 \times 13$ $\newline$ $y = 65$

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