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Algebra 1

2.8.2 Identifying Constraints in Inequalities

Algebra 12.8.2 Identifying Constraints in Inequalities

2.8.2 Identifying Constraints in Inequalities

2.8.2 • Identifying Constraints in Inequalities

Activity

Seniors in a high school student council are trying to develop a budget for the Senior Dance. The revenue from ticket sales needs to cover the cost of the meals and entertainment and also make a profit of at least $200 to be contributed to the school.

Here is some information they have gathered:

  • Last year, 120 people attended. It was a success and is expected to be even bigger this year. Up to 200 people will attend.
  • There needs to be at least 1 chaperone for every 20 students.
  • The ticket price cannot exceed $20 per person.

Here are some inequalities the seniors wrote about the situation. Each letter stands for one quantity in the situation. Determine what is meant by each letter in 1 – 4.

1.

t ≤ 20 t ≤ 20

2.

120 ≤ p ≤ 200 120 ≤ p ≤ 200

3.

p t − m ≥ 200 p t − m ≥ 200

4.

c ≥ p 20 c ≥ p 20

Are you ready for more?

Extending Your Thinking

Kiran says we should add the constraint t≥0t≥0.

1.

What is the reasoning behind this constraint?

2.

What other “natural constraint” like this should be added?

Self Check

A zookeeper feeds the tigers a meal of rabbits and chickens. The average rabbit weighs 4 pounds, and the average chicken weighs 5 pounds. Each tiger must eat at least 15 pounds of meat per day.The zookeeper writes the inequality 4x+5y≥154x+5y≥15 to represent a tiger’s daily diet. What is meant by the letter yy in the inequality above?

Additional Resources

Translate to an Inequality

To translate English sentences into inequalities, we need to recognize the phrases that indicate the inequality. Some words are easy, like “more than” and “less than.” But others are not as obvious. The table shows some common phrases that indicate inequalities.

>> ≥≥ << ≤≤
is greater than
is more than
is larger than
exceeds 		is greater than or equal to
is at least
is no less than
is the minimum		 is less than
is smaller than
has fewer than
is lower than		 is less than or equal to
is at most
is no more than
is the maximum

Example

Translate each phrase to an inequality.

Twenty-seven less than xisatleast⏟xisatleast⏟ 48 x−17≥48x−17≥48

"is at least" means ≥≥

5 more than zislowerthan⏟zislowerthan⏟ 52 z+5<52z+5<52

"is at least" means ≥≥

Try it

Translate to an Inequality 

Translate the following sentences into inequalities.

1.

Nineteen less than pp is no less than 47.

2.

Four more than aa is at most 15.

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