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If
x and
y vary directly and
y is 56 when
x is 7 , find
y when
x is 6 .
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $56$ when $x$ is $7$ , find $y$ when $x$ is $6$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

vary directly and

y

is

56

when

x

is

7

, find

y

when

x

is

6

.

\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 of Variation: Use the given values to find the constant of variation $k$ . We know that $y = 56$ when $x = 7$ . Substitute these values into the direct variation equation to find $k$ . $56 = k \times 7$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $7$ to isolate k. $\newline$ $k = \frac{56}{7}$ $\newline$ $k = 8$
Write Updated Equation: Write the direct variation equation with the found value of $k$ . Now that we know $k = 8$ , the direct variation equation is $y = 8x$ .
Find $y$ for $x=6$ : Find $y$ when $x = 6$ using the direct variation equation. $\newline$ Substitute $x = 6$ into the equation $y = 8x$ to find $y$ . $\newline$ $y = 8 \times 6$ $\newline$ $y = 48$

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