Writing Systems of Inequalities

A school has 1,200 concert tickets for sale. Some of the tickets are for reserved seats (r), and the rest are for general admission (g). At most, 500 reserved-seat tickets can be sold.

• $r+g\le1200$
  $r\ge500$
  

• $r+g\ge1200$
  $r\le500$
  

• $r+g\ge1200$
  $r\ge500$
  

• $r+g\le1200$
  $r\le500$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

A clothing store sells pants and shirts.

The store can buy up to a total of 500 pants and shirts each month. The store wants to buy at least as many shirts as pants. The store wants to buy at least 100 pants each month.

• $p\ge100$
  $s+p\le500$
  $s\le p$
  
  

• $s+p\ge500$
  $s\ge p$
  $p\ge100$
  

• $s+p\le500$
  $s\ge p$
  $p\ge100$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.12

Jordan works for a landscape company during his summer vacation. He is paid $12 per hour for mowing lawns and $14 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $250 this week. If m represents the number of hours mowing lawns and g represents the number of hours planting gardens, which system of inequalities could be used to represent the given conditions?

• 
  

  $m+g\le40$
  

  $12m+14g\ge250$
  

• $m+g\ge40$
  $12m+14g\le250$
  

• $m+g\le40$
  $12m+14g\le250$
  

• $m+g\ge40$
  $12m+14g\ge250$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

Gretchen has $50 that she can spend at the fair. Ride tickets cost $1.25 each and game tickets cost $2 each. She wants to go on a minimum of 10 rides and play at least 12 games. Which system of inequalities represents this situation when r is the number of ride tickets purchased and g is the number of game tickets purchased?

• $1.25r+2g<50$
  $r\le10$
  $g>12$
  

• $1.25r+2g\le50$
  $r\ge10$
  $g\ge12$
  

• $1.25r+2g\le50$
  $r\ge10$
  $g>12$
  

• $1.25r+2g<50$
  $r\le10$
  $g\ge12$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

A hockey team has at least 30 members. The team wants to purchase a mixture of pullovers and quarter zips so that each team member receives either a pullover or a quarter zip.
- The hockey team has a budget of $816
- Each pullover (x) costs $32 and each quarter zip (y) costs $54

• 
  

  $x-y\le30$
  

  $32x+54y\ge816$
  

• $x-y\ge30$
  $32x+54y\le816$
  

• $x+y\le30$
  $32x+54y\ge816$
  

• $x+y\ge30$
  $32x+54y\le816$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

Gianna and Casper knit hats (x) and scarves (y). Hats take 3 hours of work to make; scarves take 2 hours of work to make. Hats require 200 yards of yarn; scarves require 150 yards of yarn. Choose two inequalities to represent the constraints for x and y. Gianna and Casper can dedicate no more than 24 hours per week to making hats and scarves, and they will buy a total of 4400 or fewer yards of yarn per week.

• $2x+3y\le24$

• $3x+2y\le24$

• $3x+2y\ge24$

• $150x+200y\le4400$
  

• $200x+150y\le4400$

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

Karen is buying supplies for a party. She plans to spend at least $100 on food (f), and at least $50 on party favors (p). She can spend no more than $250 total on food and party favors combined.

• $f\ge50$
  $p\ge100$
  $f+p\le250$
  

• $p\ge50$
  $f\ge100$
  $f+p\le250$
  

• $f\le50$
  $p\ge100$
  $f+p\le250$
  

• $f\le100$
  $p\ge50$
  $f+p\le250$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

Matthew wants to sell laptops and smartphones. He wants to sell at least 12 total devices and make at least $4500 to cover expenses and turn a profit. Laptops (x) sell for $425 and smartphones (y) sell for $125.

• x + y = 12

  425x + 125y = 4500

• $x+y\le4500$
  $425x+125y\le12$
  

• $x-y\le12$
  $425x+125y\ge4500$
  

• $x+y\ge12$
  $425x+125y\ge4500$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

Kim wants to earn at least $65 from her two jobs next week. At most, she can work 15 hours. Her first job (x) pays $5 per hour, and her second job (y) pays $7 per hour. Which system of inequalities describes Kim's situation?

• x + y > 15

  5x + 7y < 65

• $x+y\le15$
  $5x+7y\ge65$
  

• $x+y\le65$
  $5x+7y\ge15$
  

• x + y > 65

  5x + 7y < 15

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

A company wants to purchase two types of lightbulbs: CFL (compact fluorescent) and LED (light emitting diode). The cost of each CFL bulb is $2, and the cost of each LED bulb is $20. The company must purchase a total of 800 lightbulbs, can spend at most $5000 on lightbulbs, and wants to purchase as many LED bulbs as possible. Let L represent the number of LED bulbs purchased, and C represent the number of CFL bulbs purchased.

• 2C + 20L = 800
  

  $C+L\le5000$
  

• 20C + 2L = 800
  $C+L\le5000$
  

• C + L = 800
  $2C+20L\le5000$
  

• C + L = 800
  $20C+2L\le5000$
  

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6