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If $x$ and $y$ are in direct proportion and $y$ is $28$ when $x$ is $4$ , find $y$ when $x$ is $3$ .

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

are in direct proportion and

y

is

28

when

x

is

4

, find

y

when

x

is

3

.

Establish Relationship: Establish the direct variation relationship between $x$ and $y$ . Since $x$ and $y$ are in direct proportion, we can write the relationship as $y = kx$ , where $k$ is the constant of proportionality.
Find Constant of Proportionality: Use the given values to find the constant of proportionality $k$ . We know that $y = 28$ when $x = 4$ . Substituting these values into the direct variation equation gives us $28 = k \times 4$ .
Solve for $k$ : Solve for $k$ . $\newline$ Divide both sides of the equation by $4$ to isolate $k$ . $\newline$ $\frac{28}{4} = \frac{(k \times 4)}{4}$ $\newline$ k = $7$
Write Equation with $k$ : Write the direct variation equation with the found value of $k$ . Now that we know $k = 7$ , the direct variation equation is $y = 7x$ .
Find $y$ for $x = 3$ : Find $y$ when $x = 3$ using the direct variation equation. $\newline$ Substitute $x = 3$ into the equation $y = 7x$ to find $y$ . $\newline$ $y = 7 \times 3$ $\newline$ $y = 21$

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