Question

If y varies directly as x and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this relation?

Answer 1

 y varies directly as x, it can be written as:

y α x

To change it into an equality, we insert a constant of proportionality, k.

y = kx

It was stated that y is 400 when x is r ans that y is r when x is 4. We find the constant of variation, k, as follows:

400 = kr ------> equation 1
r = 4k ---------> equation 2

400 = k (4k)
400 = 4k²
k = 10

Answer 2

The  numeric constant of variation in this relation is 40

If y varies directly as x, this is expressed as;

$y \alpha \ x \\y = kx$

k is the constant of proportionality

If y is 400 when x is r, then;

400 = kr

k = 400/r .................. 1

If y is r when x is 4, then;

r = 4k

k = r/4 ............................2

Equate equation 1 and 2

400/r = r/4

r² = 1600

r = √1600

r = 40

Hence the  numeric constant of variation in this relation is 40

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