Question

When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?

Answer 1

Question:

When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?

xpmy=8

xy/pm=8

xpm/y=0.5

x/pmy=0.5

Answer:

The equation models the situation is $\frac{x y}{p m}=8$

Solution:

Given that  

x is 2, y is 4, p is 0.5, and m is 2

x varies directly with the product of p and m

x varies inversely with y

$\text {Product of } p \text { and } m=p \times m=p m$

x varies directly with the product of p and m

$=>x \propto p m$ ---- eqn 1

As x varies inversely with y,

$=>x \propto \frac{1}{y}$   ----- eqn 2

From (1) and 2, we can say that

$x \propto \frac{p m}{y}$

$\Rightarrow x=k \frac{p m}{y}$

where k is constant of proportionality

$\Rightarrow \frac{x y}{p m}=k$   ---- eqn 3

On substituting given values of x = 2, y = 4, p = 0.5 and m= 2 in eqn (3) we get

$\frac{x y}{p m}=\frac{2 \times 4}{0.5 \times 2}=k$

$\begin{array}{l}{\frac{x y}{p m}=\frac{8}{1}=k} \\\\ {=>\frac{x y}{p m}=8}\end{array}$

Hence correct option is second that is $\frac{x y}{p m}=8$

Answer 2

Answer:

B

Step-by-step explanation: