Question

Cindy's nose is 1.9 inches long and her foot is 9.5 inches long. If Sandy's nose is 2.1 inches long, how long is her foot? (Assume nose and foot length are proportional.)

Answer 1

The foot length of Sandy is 10.5 inches

Solution:

Assume nose and foot length are proportional

Therefore,

$\text{ nose length } \propto \text{ foot length }$

Let "n" be the nose length and "f" be the foot length

Then,

$n \propto f$

n = kf ------ eqn 1

Where "k" is the constant of proportionality

Cindy's nose is 1.9 inches long and her foot is 9.5 inches long

n = 1.9 inches'

f = 9.5 inches

Substitute these in eqn 1

$1.9 = k(9.5)\\\\k = \frac{1.9}{9.5} = 0.2$

Thus k = 0.2

Sandy's nose is 2.1 inches long, we have to find the foot length

n = 2.1

k = 0.2

f = ?

Substitute these in eqn 1

$2.1 = 0.2 \times f\\\\f = \frac{2.1}{0.2} = 10.5$

Thus foot length of Sandy is 10.5 inches