Question

Find y when x=21/2, if y varies inversely as x and x=5 when y=3

A. 2.5/3=3/4;6
B. 2.5/3=3/4;3
C. 2.5/3=5/3;6
D. 2.5/3=5/4;3

Answer 1

y varies inversely as x:
y=C/x
C: Constant

Cross multiplication
yx=C

x=5 when y=3
Replacing in the equation above:
(3)(5)=C

when x=2 1/2=2+0.5→x=2.5, y=?
xy=C
(2.5)(y)=C

Equaling the two equations:
C=C
(2.5)(y)=(3)(5)
2.5/3=5/y

Solving for y. Dividing both sides of the equation by 2.5:
(2.5)(y)/(2.5)=(3)(5)/(2.5)
y=6

Answer:
2.5/3=5/6