Inequalities in the Real World

Theme: Band

Greater Than

1. Mr. Linquist is trying to order food for the band banquet. There are 200 band kids and they are expected to bring at least one parent. If he wants to order more food than is needed how much should he order (f)?

Greater Than or Equal To

2. Mr. Linquist is trying to figure out how many rows of bleachers we need for the Pep Rally. One row of bleachers fits 15 people. Write an inequality to find the number of rows of bleachers (x) that are needed for the Pep Rally if there are 200 people in band.

Less Than

3. In the UIL Band competition, the CHS Band has to do a marching show in under four minutes. If it takes one minute to warm up and thirty-seconds to get the props out on the field, how many minutes (x) do they have left to complete the marching show in order to not be disqualified?

Less Than or Equal To

4. We are trying to figure out how many songs we can play at a concert so that it's not too long or too short. If each song is three minutes (x) and we have to have one minute to switch out in between each band and we only have 30 minutes. At most, how many songs can we play total between all three bands in 30 minutes?

Absolute Value

5. The standard band uniform was designed to fit kids that are 5 feet tall however, kids will still fit as long as they are greater than 5 inches away from 5 feet tall. What is the range of height in inches (h), that a kid can fit in that band uniform?

Multi-Step

6. As a band we have to practice at least three hours a week. If this week, the Clarinet section (c) has practiced 30 minutes more than the Trombones, the Trumpets (t) have practiced 15 more minutes than the Clarinets, and the rest of the band (r) has practiced a total of 1 hour. At least, how much (minutes) have the Trombones (b) practiced?

Answers

1. f>400


2. 15x≥200

x≥14


3. 1.5+x<4

x<2.5


4. 3x+3≤30

x≤9


5. |h-60|≤5

-5≤h-60≤5

+60

55≤h≤65


6.

c= 30+b

t= 15+(30+b)

r= 60

b= trombones


(30+b)+b+(15+30+b)+60≥180

135+3b≥180

-135

3b≥45

3b/3, 45/3

b≥15