Question

Suppose a various jointly as b and c, when a = 14, b = ⅔ and c=⅙. What is the value of a when b = 1/9 and c= ½ ? A 12 B 126 С 252 D 7

Answer 1

The variable a varies jointly with b and c. We can assume there is a constant of proportionality between a and b and c as:

`a=k\cdot b\cdot c`

We know that when b=2/3 and c=1/6, a is equal to 14. Then we can calculate k as:

`\begin{gathered} a=k\cdot b\cdot c \\ 14=k\cdot(2)/(3)\cdot(1)/(6) \\ 14=k\cdot(2)/(18) \\ k=14\cdot(18)/(2) \\ k=126 \end{gathered}`

Then, when b=1/9 and c=1/2 we will get:

`\begin{gathered} a=126\cdot b\cdot c \\ a=126\cdot(1)/(9)\cdot(1)/(2) \\ a=(126)/(18) \\ a=7 \end{gathered}`

Answer: a = 7 [option D]