Unit 2: Expressions, Equations, and Inequalities STUDY GUIDE
Tyson and Kelsey are planning on meeting at the bowling alley. Tyson arrived first and chose to pay $4.50 for each game,
which includes his shoe rental. Kelsey came later, and she decided to pay the $3 fee for rental shoes and then pay $3 for
each game bowled. Use this information to answer questions 1 and 2.
1. Write an expression for the cost of bowling for each person. Be sure to define your variables.
2. Write and solve an equation that shows when the two costs are equal.
3. Nicki Jo pays $3.50 to watch her sister’s volleyball games. She has paid a total of $31.50 to watch her sister play
this year. Write an equation that will answer how many games Nicki Jo has watched. Then solve your equation.
4. Solve and check each equation. Round answers to the nearest tenth.
a. 3x + 10x + 2 = 92
b. 2t + (-6t) - 6 = 2
c. 102 = 8a + 5a - 3a
5. Find the change in y, the change in x, and the slope of the line graphed below.
6. Plot (3, 1) and (5, 5) on a coordinate grid. Then determine the change in y, the change in x, and the slope of the
line between the two points.
7. Shandeen bought a powdered drink mix so that she could make a sports drink to take with her to her martial arts
lessons. The table below shows the amount of drink mix remaining in the container after her first five games.
Game
Amount Left
0
32 Scoops
1
30 Scoops
2
28 Scoops
3
26 coops
a. If the pattern continues, how much drink mix will remain in the container after 10 games?
b. Let n represent the number of games in which Shandeen has played. Write and solve an equation to answer the
question, “When will Shandeen use all of the drink mix in the container?”
8. Which of the equations below are examples of direct variation? Explain your choices.
y = 2x
y = 3x + 5
y = 12_ x
6x = y
9. Which of the following graphs represents direct variation? Explain your reasoning.
a.
b.
10. Sara has no more than $75 dollars to spend on balloons and a cake for her sister’s birthday party. Balloons cost
$3.00 each and the cake cost $30.00. Write and solve an inequality to determine how many balloons Sara can
purchase. Graph the solution to the inequality.
Rodney is racing his older brother. They are going to race for one mile, which is equal to 5,280 feet. Since Rodney’s
older brother is faster than him, Rodney will be given a 200 feet head start. Rodney is able to run at a constant speed of 8
miles an hour and his older brother can run at a constant speed of 12 miles per hour.
A. Write an and solve an equation that will help you figure out how long it will take Rodney to finish the race. Choose a
variable and define your variable by telling what it represents.
B. Who will win the race? Give evidence to support your answer