Question

Two quantities, Pand Q, are connected by

the relationship P= kQ+ c, where k and c
are constants. Q= 60 when P= 10 and
Q= 240 when P= 100.
Find the equation connecting P and Q.

Answer 1

P = 0.5Q - 20

Explanation:

P = kQ + c

substitute Q = 60 , P = 10 into the equation

10 = 60k + c → (1)

substitute Q = 240, P = 100 into the equation

100 = 240k + c → (2)

subtract (1) from (2) term by term to eliminate c

90 = 180k ( divide both sides by 180 )

`(90)/(180)` =
`(1)/(2)` = 0.5 = k

substitute k = 0.5 into (1) and solve for c

10 = 60(0.5) + c

10 = 30 + c ( subtract 30 from both sides )

- 20 = c

then

P = 0.5Q - 20