Question

Assume that y varies inversely as x. Find x when y= 6 if y = 4.2 when x = 10.

x =

Answer 1

Assume that y varies inversely as x

that means

\[ y = \frac{k}{x} \]where k is some number. to find k, we use the info they gave you:
y = 4.2 when x = 10.
replace y with 4.2 and x with 10 in the formula:
\[ 4.2 = \frac{k}{10} \]
"solve" for k, by multiplying both sides by 10:
\[ 4.2 \cdot 10= \frac{k}{10}\cdot 10\\ 42=k \]

k is 42, so your formula is
\[ y = \frac{42}{x} \]

Now Find x when y= 6

Answer 2

my bad, i stopped reading after "when y=6"

Answer 3

replace y with 6 in the formula
\[ 6 = \frac{42}{x} \]
multiply both sides by x (to get the x "up top")
\[ 6x = \frac{42}{x} \cdot x \\ 6x=42\]
now divide both sides by 6 to find x
x= 42/6