Functions
Solving Equations and Inequalities
Systems
Word Problems
100
The function f is defined by the equation f(x)=100x+2 . What is the value of f(x) when x=9?
902
100
Which of the following is a solution to the inequality
7x-13<12
a. x=4 b. x=3.6 c. x=0
c. x=0
100
Which of the following ordered pairs (x,y) satisfies the inequality (select all that apply).
3x-2y<10
a. (1,-3) b. (0,-5) c. (-2,0)
a and c
100
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account?
x <12
200
D
200
What is the value of m that satisfies the equation
37=4m-14
m=12.75
200
Which of the following ordered pairs (x,y) satisfies the inequality
-3x+4y>18
a. (-1,8) b. (-2,3) c. (-5,1)
a. (-1,8) and c. (-5,1)
200
Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal?
x>=12
300
Write your answer as an ordered pair.
(0,8)
300
What is the solution to the following equation?
(3x-4)-(8x+12)=0
x = -3.2
300
A music store sells a total of 27 used trumpets and clarinets in one month. They charge $149 for trumpets and clarinets cost $99. If the total sales were $3223, write a system of equations that can be used to determine how many of each instrument the store sold using c for clarinets and t for trumpets.
c + t = 27
99c + 149t = 3223
300
Kelly is in charge of the social committee at her job. She hired a DJ for the company holiday party. The DJ charges $125 per hour plus a $175 set up/break down fee. Her company has budgeted $550 for the DJ. How many hours should Kelly schedule the DJ for to stay within the company budget?
3 hours
400
As part of a science project on evaporation, Amaya measured the height of a liquid in a container over a period of time. The function f(x)=33-0.18x gives the estimated height, in centimeters (cm), of the liquid in the container x days after the start of the project. What is the best interpretation of 33 in this context?
The estimated height, in cm, of the liquid at the start of the project
400
Which of the following is a solution to the inequality
-3(p-7)>=21
a.0 b.10 c.20
a. 0
400
Marsha is buying plants and soil for her garden. The soil cost $4 per bag, and the plants cost $10 each. She wants to buy at least 5 plants and can spend no more than $100. Write a system of inequalities that represents this situation where x represents the number of bags of soil and y represents the number of plants.
4x+10y≤100
y≥5
400
The new car wash in town charges $25 for each car and $40 for each truck. The owner wants to earn no less than $7,000 per week from sales. If 100 cars go through one week, how many trucks must be washed so the company can meet the constraints?
They must wash 113 trucks so that they meet the constraints.
500
V(t)=1450+77t
The value of an antique car in a certain year can be modeled by the function V above, where V(t) is the value t years after the year 1980.
What is the best interpretation of the equation V(50)=5300
The value of the antique car is predicted to be $5300 in the year 2030.
500
What are the values of x that satisfy the inequality
-(5x+4)-16<4x-(2x-5)+10
x>-5
500
Two kinds of tickets to an outdoor concert were sold: lawn tickets and seat tickets. Fewer than 400 tickets in total were sold. Lawn tickets cost $30 each and seat tickets cost $50 each. The organizers want to make at least $14,000 from ticket sales. Write a system of inequalities where x represents the number of lawn tickets and y represents the number of seat tickets.
x+y<400
30x+50y≥14000
500
A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?
5 ducks 6 goats
600
3500
600
DAILY DOUBLE!
What value of x satisfies the equation below?
10p+9-11-p=-2(2p+4)-3(2p-2)
600
Mrs. Greenway grows onions and potatoes to sell at the local Farmer's Market. The price of 5 onions and 2 potatoes is $4.35, and the price of 1 onion and 4 potatoes is $5.37. Based on that pricing, what is the cost of 3 onions and 7 potatoes?
$9.86
600
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 shirts, then how many of each kind did she buy?
2 fancy, 5 plain