Chapter 3.2, Problem 3GP

To determine

To find:

Zero, domain, and range of the given equation $y=1.5x-45$ and to write its mean in the context of given situation.

Answer to Problem 3GP

Zero of the equation is $x=30$ and it means that minimum more than 30 candies should be sold surely to get the profit accordingly.

Also, domain of this relation is $\{30,31,32,33\dots \}$ and range is $\{0,1.5,3,4.5,6,7.5,\dots \mathrm{..}\}$ .

Explanation of Solution

Given information:

A`s class is selling candy to raise money for a class trip. They paid $45 for the candy, and they are selling each candy bar for $1.50. The function, $y=1.5x-45$ represents students profit y when they sell x candy bars.

Concept used:

Zero of an equation is obtained by putting it equal to 0 and then solving it for independent variable x .

Also set of all values of x is its domain and set of all values of y is its range.

Calculation:

Plug in y = 0 in and on solving it for x ,

  $\begin{array}{l}0=1.5x-45\\ \Rightarrow 1.5x=45\\ \Rightarrow x=\frac{45}{1.5}=30\end{array}$

So, only zero of the equation is $x=30$

  $.$

As x are the number of candies sold and 30 are minimum candies, to start getting profit. So, x may be greater or equal to 30. So, domain of this function will be an infinite set $\{30,31,32,33\dots \}$ and by selling a single candy, it will be a profit of $1.5, so its range will be the set of all multiples of 1.5 as $\{0,1.5,3,4.5,6,7.5,\dots \mathrm{..}\}$ .

Conclusion:

Value $x=30$ means that minimum more than 30 candies should be sold surely to get the profit accordingly. Also, domain of this relation is $\{30,31,32,33\dots \}$ and range is $\{0,1.5,3,4.5,6,7.5,\dots \mathrm{..}\}$ .