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SAT Math : How to find inverse variation

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Example Question #1 : How To Find Inverse Variation

A school's tornado shelter has enough food to last 20 children for 6 days. If 24 children ended up taking shelter together, for how many fewer days will the food last?

Possible Answers:

Correct answer:

Explanation:

Because the number of days goes down as the number of children goes up, this problem type is inverse variation. We can solve this problem by the following steps:

20*6=24*x

120=24x

x=120/24

x=5

In this equation, x represents the total number of days that can be weathered by 24 students. This is down from the 6 days that 20 students could take shelter together. So the difference is 1 day less.

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Example Question #2 : How To Find Inverse Variation

Find the inverse equation of:

$\displaystyle 3y-2x=20$

Possible Answers:

$\frac{2x+20}{3}=y$ $\displaystyle \frac{2x+20}{3}=y$

$\frac{3x-20}{2}=y$ $\displaystyle \frac{3x-20}{2}=y$

$\frac{1}{2}x+10=y$ $\displaystyle \frac{1}{2}x+10=y$

$\frac{2x-20}{3}=y$ $\displaystyle \frac{2x-20}{3}=y$

Correct answer:

$\frac{3x-20}{2}=y$ $\displaystyle \frac{3x-20}{2}=y$

Explanation:

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

$\frac{3x-20}{2}=y$ $\displaystyle \frac{3x-20}{2}=y$

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Example Question #3 : How To Find Inverse Variation

Find the inverse equation of $\displaystyle 5x-4y=18$.

Possible Answers:

$x=\frac{4y+18}{5}$ $\displaystyle x=\frac{4y+18}{5}$

$y=\frac{4x+18}{5}$ $\displaystyle y=\frac{4x+18}{5}$

x=y $\displaystyle x=y$

$y=\frac{x+18}{4}$ $\displaystyle y=\frac{x+18}{4}$

$y=\frac{4x+5}{18}$ $\displaystyle y=\frac{4x+5}{18}$

Correct answer:

$y=\frac{4x+18}{5}$ $\displaystyle y=\frac{4x+18}{5}$

Explanation:

$\displaystyle 5x-4y=18$

1. Switch the $\displaystyle x$ and $\displaystyle y$ variables in the above equation.

$\displaystyle 5y-4x=18$

2. Solve for $\displaystyle y$:

$\displaystyle 5y-4x=18$

$\displaystyle 5y-4x+4x=18+4x$

$\displaystyle 5y=4x+18$

$\frac{5y}{5}=\frac{4x+18}{5}$ $\displaystyle \frac{5y}{5}=\frac{4x+18}{5}$

$y=\frac{4x+18}{5}$ $\displaystyle y=\frac{4x+18}{5}$

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Example Question #4 : How To Find Inverse Variation

$\begin{matrix} & \x\ & \y\ & \\ & \\ & \end{matrix}$ $\displaystyle \begin{matrix} & \x\ & \y\ & \\ & \\ & \end{matrix}$When x=2 $\displaystyle x=2$, y=18 $\displaystyle y=18$.

When x=9 $\displaystyle x=9$, y=4 $\displaystyle y=4$.

If $\displaystyle x$ varies inversely with $\displaystyle y$, what is the value of $\displaystyle y$ when x=12 $\displaystyle x=12$?

Possible Answers:

y=6 $\displaystyle y=6$

y=3 $\displaystyle y=3$

y=1 $\displaystyle y=1$

y=1.5 $\displaystyle y=1.5$

y=x $\displaystyle y=x$

Correct answer:

y=3 $\displaystyle y=3$

Explanation:

If $\displaystyle y$ varies inversely with $\displaystyle x$, $y=\frac{K}{x}$ $\displaystyle y=\frac{K}{x}$.

1. Using any of the two x,y $\displaystyle x,y$ combinations given, solve for $\displaystyle K$:

Using (2,18) $\displaystyle (2,18)$:

$18=\frac{K}{2}$ $\displaystyle 18=\frac{K}{2}$

K=36 $\displaystyle K=36$

2. Use your new equation $y=\frac{36}{x}$ $\displaystyle y=\frac{36}{x}$ and solve when x=12 $\displaystyle x=12$:

$y=\frac{36}{12}=3$ $\displaystyle y=\frac{36}{12}=3$

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Example Question #5 : How To Find Inverse Variation

x	y
$\displaystyle 5$	$\displaystyle 4.8$
$\displaystyle 6.4$	$\displaystyle 3.75$
$\displaystyle 3$	$\displaystyle n$
$\displaystyle 20$	$\displaystyle 1.2$

If $\displaystyle y$ varies inversely with $\displaystyle x$, what is the value of $\displaystyle n$?

Possible Answers:

$\displaystyle 6$

$\displaystyle 17$

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 12$

Correct answer:

$\displaystyle 8$

Explanation:

An inverse variation is a function in the form: xy = k $\displaystyle xy = k$ or $y = \frac{k}{x}$ $\displaystyle y = \frac{k}{x}$, where $\displaystyle k$ is not equal to 0.

Substitute each $\left ( x,y \right )$ $\displaystyle \left ( x,y \right )$ in xy = k $\displaystyle xy = k$.

$\displaystyle 5(4.8) = 24$

$\displaystyle 6.4(3.75) = 24$

$\displaystyle 20(1.2) = 24$

Therefore, the constant of variation, $\displaystyle k$, must equal 24. If $\displaystyle y$ varies inversely as $\displaystyle x$, $\displaystyle 3n$ must equal 24. Solve for $\displaystyle n$.

3n = 24 $\displaystyle 3n = 24$

n = 8 $\displaystyle n = 8$

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x	y
\(\displaystyle 5\)	\(\displaystyle 4.8\)
\(\displaystyle 6.4\)	\(\displaystyle 3.75\)
\(\displaystyle 3\)	\(\displaystyle n\)
\(\displaystyle 20\)	\(\displaystyle 1.2\)

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SAT Math : How to find inverse variation

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #3 : How To Find Inverse Variation

Example Question #4 : How To Find Inverse Variation

Example Question #5 : How To Find Inverse Variation

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