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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q.466. (page 741)

If $y$ varies inversely as $x$ when $y = 20$ and $x = 2$ , find $y$ when $x = 4$ .

Short Answer

Expert verified

The solution is $y = 10$ .

Step by step solution

01

Step 1. Given information.

$y$ varies inversely $x$ , when $y = 20$ and $x = 2$ .

02

Step 2. Write the formula for inverse variation.

$y = \frac{k}{x}$

03

Step 3. Solve for k.

The required equation is $y = \frac{k}{x}$ .

Substitute $y = 20$ and $x = 2$ :

$y = \frac{k}{x} k = x y k = 20 脳 2 k = 40$

04

Step 4. Solve for y, by substituting x=4 and k=40 in the given equation y=kx.

$y = \frac{k}{x} y = \frac{40}{4} y = 10$

05

Step 5. Simplified answer.

Hence, the value of $y$ is $10$ .

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