Exercise 4 Page 149

Practice makes perfect

a Let x be the number of packages of hot dogs and y be the number of packages of buns. With this, we will write three inequalities that represent the situation. Let's first write an inequality for the number of packages making an organized table.

Packages of hot dogs		Packages of Buns
Verbal Expression	Algebraic Expression	Verbal Expression	Algebraic Expression
Minimum number of hot dogs	40	Minimum number of buns	40
Number of hot dogs in one package	10	Number of buns in one package	8
Minimum number of packages of hot dogs	40/10= 4	Minimum number of packages of buns	40/8= 5
Number of packages of hot dogs is at least 4.	x≥ 4	Number of packages of buns is at least 5.	y≥ 5

Next, we will write an inequality for the cost proceeding in the same way.

Verbal Expression	Algebraic Expression
Cost of x packages of hot dogs ($)	3.5 x
Cost of y packages of buns ($)	2.5 y
Total cost is less than or equal to $35.	3.5 x+ 2.5 y≤ 35

Now we have three inequalities to write a system. x ≥ 4 & (I) y ≥ 5 & (II) 3.5x+2.5y ≤ 35 & (III) Let's begin by drawing the first inequality. We will first find the boundary line by replacing the inequality sign with the equals sign.

cc Inequality I &Boundary Line I x ≥ 4 &x = 4 The boundary line of Inequality I is a vertical line that passes through the point (4,0). Since the number of packages cannot be negative the line will be bound by the axes. It will also be solid because the inequality is non-strict. Let's draw it!

The inequality says that the points with the x-coordinates greater than or equal to 4 are solutions. Therefore, we will shade region to the right of the boundary line.

We will graph the second inequality thinking in the same way. cc Inequality II &Boundary Line II y ≥ 5 & y = 5 The boundary line will be a horizontal line that passes through the point (0,5). We will shade the region above the line because the points with the y-coordinates greater than or equal to 5 are solutions to the inequality.

Finally, we will graph the last inequality. cc Inequality III &Boundary Line 3.5x+2.5y ≤ 35 & 3.5x+2.5y = 35 To graph the boundary line, we will find its intercepts. We will substitute y= 0 for the x-intercept and x= 0 for the y-intercept.