Question

On Naomi's cell phone plan, the amount she pays each month for international text messages is proportional to the number of international texts she sends that month. Last month, she paid $3.20 for 16 international texts.
A. What is the constant of proportionality in this proportional relationship?

B. Write an equation to represent this proportional relationship. Make sure to define the variables you use.

Answer 1

A) The constant of proportionality in this proportional relationship is $k = \frac{y}{x}$

B) The equation to represent this proportional relationship is y = 0.2x

Solution:

Given that,

The amount Naomi pays each month for international text messages is proportional to the number of international texts she sends that month

Therefore,

This is a direct variation proportion

$\text{ amount paid each month } \propto \text{ number of international texts sent that month}$

Let "y" be the amount that Naomi pays each month

Let "x" be the number of international texts she sends that month

Therefore,

$y \propto x$

y = kx -------- eqn 1

Where, "k" is the constant of proportionality

Thus the constant of proportionality in this proportional relationship is:

$k = \frac{y}{x}$

Last month, she paid $3.20 for 16 international texts

Therefore,

y = 3.20

x = 16

Thus from eqn 1,

$3.20 = k \times 16\\\\k = \frac{3.20}{16}\\\\k = 0.2$

Substitute k = 0.2 in eqn 1

y = 0.2x

The equation would then be y = 0.2x