Two-Variable 1

Two Variable Inequalities

Enrique Borroto

MAT 222 Week 1 Assignment

Stacie Williams

March 09, 2014

Two-Variable 2

Two Variable Inequalities

For this assignment, this week’s paper will examine a practical application of two

variable inequalities. It will demonstrate the working of dependent and independent

variables as well as show graphic representations of the solutions for each problem within the

paper. Due to the specific inequality, the graphs and solutions will demonstrate a range of

possible outcomes that can work in the specific situation. The problem that will be worked on in

this paper is problem #68 on pg. 539 of Intermediate Algebra The problem itself is as follows:

“Shipping restrictions. The accompanying graph shows all of the possibilities for the number of

refrigerators and the number of TVs that will fit into an 18-wheeler.

a) Write an inequality to describe this region.

b) Will the truck hold 71 refrigerators and 118 TVs?

c) Will the truck hold 51 refrigerators and 176 TVs?” (Intermediate Algebra, 2012)

The diagram on page 68 is showing the refrigerators on the x axis and the TVs on the y

axis. There are two points on the graph, (0, 330) and (110, 0), so we can compute the slope of

this line.

The slope is: y^1-y^2/x^1-x^2= 330-0/0-110= 330/-110= So the slope is= -33/11= -3

The point slope for of a linear equation will now be used in this equation. The steps on how to

perform the method to get a linear inequality are as follows:

y - y1 = m(x - x1) Start with the point slope form

y - 330 = -33/11(x - 0) Substitute the slope for m and (330, 0) for the x and y.

y= -33/11x + 330 Use distributive property and then add 330 to both sides.

Two-Variable 3

11y = -33 + 3630 Multiply both sides by 11.

33x +11y < 3630 Add 33x to both sides and change to less than or equal to symbol.

The graph will have a solid line rather than a dotted line indicating that points on the line itself will be part of this solution set.This will be true anytime the inequality symbol has the

equal to bar on it.

-Will the truck hold 71 refrigerators and 118 TVs?

33x +11y < 3630

33(71) + 11(118) ≤ 3630

2343 + 1298 ≤ 3630

3641 ≤ 3630 This is a false statement so the container cannot hold the amount stated.

- Will the truck hold 51 refrigerators and 176 TVs?

33x +11y < 3630

33(51) + 11(176) ≤ 3630

1683 + 1936 ≤ 3630

3619 ≤ 3630 This shipment is possible.

With all test points shown and demonstrated, the only thing left to do is to finish the other two questions for this paper.

-The Burbank Buy More store is going to make an order which will include, at most, 60

refrigerators. What is the maximum number of TVs that could also be delivered on the same 18-

wheeler?

33x +11y < 3630 33(60) +11y < 3630 Substitute given value and multiply

Two-Variable 4

1980 +11y < 3630 Subtract 1980 on both sides

11y < 1650 Divide both sides by 11.

y < 150

-The next day, the Burbank Buy More decides they will have a television sale so they change

their order to include at least 200 TVs. What is the maximum number of refrigerators that could

also be delivered in the same truck?

33x +11y < 3630

33x +11(200) < 3630 Substitute given value and multiply

33x + 2200 < 3630 Subtract 2200 on both sides.

33x < 1430 Divide both sides by 33.

x < 43.3

Now that both problems have been resolved, the only thing left to do is conclude the paper.

In conclusion, the steps taken for the two step variable inequality shows absolute proof of

algebra as used in real world business related problems. It is certain that without such effective

measures as this two step variable inequality, the work necessary to fill and stock loads into

trucks for delivery would be a more difficult if not impossible task. Algebra has proven yet again

of its importance in everyday life and situations in terms of business as well as its power to make everything run more efficiently with less time constraints.

References

Two-Variable 5

1. 1. Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing.

Two-Variable 6