Question

guided practice
now lets practice. use the information given to answer a question.
( y ) varies directly with ( x ) and inversely with ( w ).
( y ) is 100 when ( x ) is 2 and ( w ) is 3.

find the value of ( k ), and then write a specific formula.
a. ( k = 150, y=\frac{150x}{w} )
b. ( k = 100, y=\frac{100x}{w} )
c. ( k=\frac{200}{3}, y=\frac{200x}{3w} )
d. ( k=\frac{2}{3}, y=\frac{2x}{3w} )

Explanation:

Step1: Define variation formula

$y = \frac{kx}{w}$

Step2: Substitute values to find k

$100 = \frac{k \cdot 2}{3} \implies k = \frac{100 \cdot 3}{2} = 150$

Step3: Write specific formula

$y = \frac{150x}{w}$

Answer:

A. $k=150$, $y=\frac{150x}{w}$