Answer :
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 [tex]\frac{x y}{p m}=8[/tex]
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
[tex]\text {Product of } p \text { and } m=p \times m=p m[/tex]
x varies directly with the product of p and m
[tex]=>x \propto p m[/tex] ---- eqn 1
As x varies inversely with y,
[tex]=>x \propto \frac{1}{y}[/tex] ----- eqn 2
From (1) and 2, we can say that
[tex]x \propto \frac{p m}{y}[/tex]
[tex]\Rightarrow x=k \frac{p m}{y}[/tex]
where k is constant of proportionality
[tex]\Rightarrow \frac{x y}{p m}=k[/tex] ---- eqn 3
On substituting given values of x = 2, y = 4, p = 0.5 and m= 2 in eqn (3) we get
[tex]\frac{x y}{p m}=\frac{2 \times 4}{0.5 \times 2}=k[/tex]
[tex]\begin{array}{l}{\frac{x y}{p m}=\frac{8}{1}=k} \\\\ {=>\frac{x y}{p m}=8}\end{array}[/tex]
Hence correct option is second that is [tex]\frac{x y}{p m}=8[/tex]
