Question

Daniel works at an electronics store, and he claims that the popularity of a television (measured in number of sales) is inversely proportional to its cost. If 15 customers buy a television that costs $1500, according to Daniel's theory, how many customers would buy a television that costs $2500?

Answer 1

We are given that popularity of television is inversely proportional to its cost.

let us say popularity of television is represented by "P" and cost of television by "T".

We will use a constant "k" to convert the proportionality sign to equal to (=) sign.

Thus forming the equation :

$P= \frac{k}{T}$

We are given that 15 customers buy a television that cost $1500.

plugging P=15 and T=1500, finding k,

$15= \frac{k}{1500}$

k=15*1500 = 22500

Next we have to find how many customers would buy a television that costs $2500, so here k=22500 and T=2500, plugging this in the equation we have ,

$P= \frac{22500}{2500}$

P=9

So there will be 9 customers that buy a television which costs $2500.

Answer 2

Answer: 9

Step-by-step explanation:

The equation to show inverse variation between two quantities x and y is given  by :-

$x_1y_1=x_2y_2$

Given : Daniel claims that the popularity of a television (measured in number of sales) is inversely proportional to its cost.

15 customers buy a television that costs $1500.

Let x be the number of  customers buy a television that costs $2500.

Then , we have the following equation :-

$x\times2500=15\times1500\\\\\Rightarrow\ x=\dfrac{15\times1500}{2500}=9$

Hence, 9 customers would buy a television that costs $2500.