Question

If y is directly proportional to x, and y = 56 when x = 6, what is

the value of x when y = 84?
A)6
B)9
C)13
D)15

Answer 1

B) 9

Explanation:

According to the statement, we have the following relationship:

`y \propto x`

`y = k\cdot x` (Eq. 1)

Where:

`k` - Proportionality constant, dimensionless.

`x` - Independent variable, dimensionless.

`y` - Dependent variable, dimensionless.

Such constant is eliminated by constructing this relationship:

`(y_(2))/(y_(1)) = (x_(2))/(x_(1))`

`x_(2) = \left((y_(2))/(y_(1)) \right)\cdot x_(1)` (Eq. 2)

If we know that
`y_(1) = 56`,
`x_(1) = 6` and
`y_(2) = 84`, then the value of
`x_(2)` is:

`x_(2) = \left((84)/(56) \right)\cdot (6)`

`x_(2) = 9`

Hence, the correct answer is B.