Chapter 4.2, Problem 48PFA

a.

To determine

To find: The equation in standard form that models the number of moss plants x and thyme plants y that you can buy.

Answer to Problem 48PFA

The equation is $5.5x+6y\le 330.$

Explanation of Solution

Given:

The cost per Irish moss plant is $5.50 and that per Creeping Thyme plant is $6.

Spend a maximum of $330 for the plants together. Total number of Irish moss plant that can buy is x and that of Thyme plants is y .

Calculation:

And so according to the given data, the equation can be formed as follows $5.5x+6y\le 330$ .

b.

To determine

To calculate: Which combinations of plants will not cost exactly $330 (excluding tax).

Answer to Problem 48PFA

B. 8 moss, 62 thyme.

C. 12 moss, 66 thyme.

Explanation of Solution

Given:

Cost per Irish moss plant is $5.50 and that per Creeping Thyme plant is $6.

Calculation:

For $x=8,y=62$ , we get,

  $5.5x+6y=5.5*8+6*62=416$ (1)

And for $x=12,y=66$ , we get,

  $5.5x+6y=5.5\ast 12+6\ast 66=462$ (2)

c.

To determine

To find: The graph of the equation.

Answer to Problem 48PFA

Graph.

Explanation of Solution

Given:

The equation is given as $5.5x+6y\le 330.$

Calculation:

So let's plot the graph for the equation $5.5x+6y=330.$

The graph will be as follows:

  

d.

To determine

To identify: Whether equal number of plants can be bought or not.

Answer to Problem 48PFA

No, you cannot buy equal number of plants.

Explanation of Solution

Given:

Equation of the line is $5.5x+6y=330.$

Calculation:

If you buy equal number of plants, then y will be equal to x .

So, let's plug-in $y=x$ in the equation $5.5x+6y=330.$

  $\begin{array}{l}5.5x+6x=330\\ 11.5x=330\\ x=\frac{330}{11.5}\\ x=28.6957\end{array}$

Conclusion:

x is coming out to be a floating point decimal number and number of plants has to be an integer, it cannot be a floating decimal number. And so we can conclude that x and y cannot be equal. And so you cannot buy equal number of plants.