1. Applications of Linear Inequalities

2. Look at the following word problem.
For an art exhibition, the cost of a ticket for an adult is $4 and for a child is $2. The total amount collected on Saturday was $6400.
Write an equation to model this situation.
4x+2y=6400

3. b.) How can you tell the difference?
Ashley can spend no more than $30 on buying liters of soda and bags of chips for an upcoming party. A liter of soda costs $3 and bag of chips cost $5.
a.) What is more practical - modeling this situation with an equation or an inequality?
b.) How can you tell the difference?
c.) Write the inequality, where x means # of liters of soda and y means # of bags of chips.
d.) Graph the inequality.
e.) What do all the points along the border line represent?
inequality
NO MORE THAN
3x+5y<30
Combinations exactly equal to 30

4. b.) Graph the inequality.
Luther is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under $300. A band can play for part of the time at an hourly rate of $30, and a DJ can play for the remaining time at an hourly rate of $20.
a.) Write the inequality, where x means # of hours the band will play and y means # of hours the DJ will play.
b.) Graph the inequality.
c.) Choose one point in the solution region and explain its meaning.
30x+20y<300
You can pick any ordered pair. For example, (2,8) means 2 hours
of band and 8 hours of DJ is less than $300.

5. a.) Define the variables and label each axis x = y =
A local sports equipment store makes custom skateboards and snowboards. The owner of the store insists that they make at least 12 skateboards and snowboards each day. The employees can complete no more than 30 hours worth of work each day. Each skateboard takes 3 hours to make and each snowboard takes 2 hours to make.
a.) Define the variables and label each axis
x =
y =
b.) Write a system of 2 inequalities.
c.) Graph the inequalities.
d.) What does the solution region represent?
e.) Choose one point in the solution region and explain its meaning.
skateboard
snowboard
x+y>12
3x+2y<30
All possible combinations
You can make 1 skateboard and 13 snowboards in one day