How to find inverse variation

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SAT Math › How to find inverse variation

Questions 1 - 5

1

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?

8

6

4

2

1

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.

2

Find the inverse equation of:

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

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

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

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

Explanation

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

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

3

Find the inverse equation of .

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

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

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

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

Explanation

1. Switch the and variables in the above equation.

2. Solve for :

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

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

4

$\begin{matrix} & \x\ & \y\ & \ & \ & \end{matrix}$ When , .

When , .

If varies inversely with , what is the value of when ?

Explanation

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

1. Using any of the two combinations given, solve for :

Using :

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

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

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

5

x	y

If varies inversely with , what is the value of ?

Explanation

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

Substitute each $\left ( x,y \right )$ in .

Therefore, the constant of variation, , must equal 24. If varies inversely as , must equal 24. Solve for .

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