Algebra Week 1 Flashcards
Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms.
Joe had already reserved and paid for 16 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900.
Let B represent the number of additional blocks that Joe reserves.
Which inequality describes this scenario?
a) 16 + 8B ≤ 50
b) 16 + 8B ≥ 50
c) 16 + B ≤ 50
d) 16 + B ≥ 50
What is the least amount of additional money (dollars) Joe can spend to get the rooms they need?
b) 16 + 8B ≥ 50
4500 dollars
Anand needs to hire a plumber. He’s considering a plumber that charges an initial fee of $65 along with an hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.
Let H represent the whole number of hours that the plumber works.
Which inequality describes this scenario?
a) 28 + 65H ≤ 250
b) 28 + 65H ≥ 250
c) 65 + 28H ≤ 250
d) 65 + 28H ≥ 250
What is the largest whole number of hours that Anand can afford?
c) 65 + 28H ≤ 250
6 hours
Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35 and an additional fee of $12 per class taken. Rebekah’s goal is for each customer to spend at least $100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal.
Let C represent the number of classes a customer takes.
Which inequality describes this scenario?
a) 35 + C ≤ 100
b) 35 + C ≥ 100
c) 35 + 12C ≤ 100
d) 35 + 12C ≥ 100
What is the minimum number of classes a customer can take for Rebekah to meet her goal?
d) 35 + 12C ≥ 100
6 classes
Jacque needs to buy some pizzas for a party at her office. She’s ordering from a restaurant that charges a $7.50 delivery fee and $14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60.
Each pizza is cut into 8 slices, and she wonders how many total slices she can afford.
Let P represent the number of pizzas that Jacque buys.
a) 7.50 + 14P < 60
b) 7.50 +14P > 60
c) 14 + 7.50P < 60
d) 14 + 7.50P > 60
What is the largest number of slices that Jacque can afford?
a) 7.50 + 14P <60
24 slices
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Let R represent the number of additional rolls that Sofia orders.
Which inequality describes this scenario?
a) 12 +24R ≤ 100
b) 12 + 24R ≥ 100
c) 24 + 12R ≤ 100
d) 24 + 12R ≥ 100
What is the least amount of additional money (dollars) Sofia can spend to get the sushi they need?
d) 24 + 12R ≥ 100
56 dollars
Solve for x.
7x + 39 ≥ 53 AND 16x + 15 > 31
a) x > 1
b) x ≥ 2
c) x ≤ 2
d) There are no solutions
e) All values of x are solutions
b) x ≥ 2
Solve for x.
-15x + 4 ≤ 109 OR -6x + 70 > -2
a) x ≥ -7
b) -7 ≤ x < 12
c) x <12
d) There are no solutions
e) All values of x are solutions
e) All values of x are solutions
Which of the following equations have exactly one solution?
a) 58x + 52 = -78x - 78
b) -78x + 52 = -52x - 78
c) 58x + 52 = 78x -78
d) 52x + 52 = 52x - 78
a) 58x + 52 = -78x - 78
b) -78x + 52 = -52x - 78
c) 58x + 52 = 78x -78
How many solutions does the following equation have?
-14(z-5) = -14z + 70
a) No solutions
b) Exactly one solution
c) Infinitely many solutions
c) Infinitely many solutions
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors.
How much wood does Astrid need to accommodate 2100 sailors?
280 tons
Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo’s videos is 1:5. Dagogo wants to reach a total of 9,000,000 views on his channel.
Assuming these rates continue, for how many months does Dagogo need to upload videos to get to 9,000,000 views on his channel?
20 months
How many seconds are in a day?
86,400 seconds
How many minutes are in a day?
1,440 minutes
How many seconds are in an hour?
3,600 seconds
A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (kpx) of a kitchen scene and renders another 90 kpx each minute.
The computer has rendered 960 kpx of a garden scene and renders 60 kpx more pixels each minute.
After how many more minutes will the scenes have the same amounts rendered?
14 minutes
