2.04 Solving Applications Involving Systems of Inequalities

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2.04 Solving Applications Involving Systems of Inequalities

Write a system of inequalities to model the following application problems. Then, graph the system and answer the questions about the solutions. You can make your graphs in GeoGebra and copy and paste into this document. To use GeoGebra, go to the Online GeoGebra. For instructions on how to create a graph using GeoGebra, refer to the GeoGebra Instructions in the Course Information Section of D2L.

1.The most you can work 25 hours in a week. Your babysitting job pays $12 per hour and your job at a pizza place pays $8 per hour. You need to earn more than $120 per week to cover your expenses. Write a system of inequalities to model this situation. Then graph it. Give 2 examples of solutions to this system.
System of inequalities:

Graph:

Example 1:
Example 2:

2.A candy company makes chocolate bars. The regular size bar has 1 oz of chocolate, while the king size bar has 2.5 oz of chocolate. The company makes batches of more than80 bars at a time and uses less than 150oz of chocolate for each batch. Write a system of inequalities to model this situation. Then graph it.
System of inequalities:
Graph:

Which of the following would be true for this situation? Write true or false.

A batch could consist of 90 regular bars and 20 king size bars.

A batch could have 160 total bars.

If a batch contains 30 king size bars, the greatest number of regular size bars it could have is 50.

3.You are planning a trip. You cannot be gone more than 8 days. You have two hotels from which to choose. Hotel A is a 4-star hotel and costs $125 per night and Hotel B is a 3-star hotel andcosts $80 per night. You cannot spend more than $800 on hotels. Write a system of inequalities to model this situation. Then graph the system.

System of inequalities:

Graph:

Answer the following questions:

What is the maximum number of days you can stay in Hotel A?

If you stay the maximum number of days in Hotel A, how many days could you then stay in Hotel B?

If you stay 4 days in Hotel B, what is the maximum number of days you could stay in Hotel A?

4.You are packing pairs of boxed shoes into bigger boxes for shipping. You can either fit 6 adult shoe boxes or 9 children’s shoe boxes into the bigger box. You only have 30 of the bigger boxes and, combined, you want to pack at least 180 of the pairs of shoes. Write a system of inequalities to model this situation. Then graph the system. Give 2 sample solutions.
System of inequalities:

Graph:

Sample 1:
Sample 2: