Equations/Linear Equations
Inequalities/Linear Inequalities
Proportional Relationships
Percents
Word Problems
100
-6(2x - 3) = -72
x = 7.5
100
-4x - 36 > 88
x < -31
100
What must a graph have to represent a direct proportion?
1) It must be linear (straight line).
2) It must pass through the origin.
100
What is 62% of 540?
334.8
100
Lily and Jane split $108 in a ratio of 4:2, Lily is getting more because she is older. What amount of money did Jane get? (2 points)
Jane got $36.00.
200
4x - 6 = -2(-2x + 9)
no solution
200
-1/2(5x - 18) > 24
x < -6
200
y is directly proportional to x, and y = 72 and x = 3. What is the constant of proportionality?
What is the direct proportion equation?
k = 24
y=24x
200
12 is what percent of 142?
(Round to the nearest whole percent)
8%
200
You earned an 73, 84, and 92 on your first three science quizzes. What would you need to get on your fourth science quiz to have an average of at least 85%?
x is greater than or equal to a 91% on the fourth quiz.
300
-8x - 9 = -2(4x + 3) -3
infinite solutions
300
14x - 7 + 5x - 3.5 < 10x + 7.5
x < 2
300
Is this a direct proportion equation?
If yes, what is the constant of proportionality?
0.1y=x
Yes, the constant is 10.
y=10x
300
On Valentine's Day, about 40% of the EMS students who attended school that day wore pink. If 380 students wore pink, how many students attended school that day?
950 students attended school that day.
300
During the NYC Marathon, Ms. Harrichand ran 12 miles from Staten Island to Queens in 2 hours. Then she ran 6.2 miles from Queens to Brooklyn in 1.5 hours. Finally, she ran 8 miles from Brooklyn to Manhattan in 1.75 hours. Find the average speed she ran. (Round your answer to the nearest mile per hour.)
Ms. Harrichand ran 5 miles per hour
400
8(14x - 12) = 4(x - 16)
x = 8/27
400
1/4(16x - 8) > 1/5(15x - 25)
x > -3
400
Does this table show a direct proportion?
If so, what is the constant? What is the direct proportion equation?
Not a direct proportion.
400
On Friday, Mary earned a $75 in tips working at a restaurant. Tim earned 10% more than Mary. On Saturday, Tim earned $100 in tips. What was Tim's percent of change from Friday to Saturday? Round to the nearest whole number.
21% increase
400
The ice skating rink has two different payment plans (see below). What number of months will be the breakeven point, where both plans will have cost the same amount for members and non-members?
At 3 months members and non-members will have cost the same amount.
500
6(x + 2/3) + 3x = 4x +2
x = -2/5 or -0.4
500
125 > 4.5x + 11 + 6.5x - 7
11 > x
or
x < 11
500
Kat runs 4 miles in 45 minutes. Given that her distance is directly proportional to the time she runs..
Find the constant of proportionality
Write an equation to represent the direct proportion.
Determine how many minutes it will take Kat to run 6 miles.
k = 11.25 minutes/mile
y=11.25x
It will take Kat 67.5 minutes to run 6 miles.
500
Ron buys new pucks and a stick for the hockey season. The stick costs 20% more than the pucks. If the total of both items is $176, what is the cost of the stick?
The stick is $96.
500
3/5 of the beads in a box are blue beads. The rest of the beads are red and yellow in a ratio of 1:3. The amount of blue beads is 300 more than the number of yellow beads. Fine out the amount of each color bead.
blue: 600
red: 100
yellow: 300