Writing Systems of Linear Inequalities

You can work a total of no more than 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system to represent the situation.

• x+y≤254
  5x+8y≥41
• x+41≤y
  5x+8y≥254
• x+y≤41
  5x+8y≥254
• x+y>41
  5x+8y<254

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Your tank can hold 14 gallons at most. Write a system to represent this situation.

• x+y≤14
  2x+3y≤18
• 2x+3y≤14
  x+y≤18
• 2x+y<18
  x+3y<14
• x+14≤y
  2x+3y≤18

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

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 to model the situation.

• 4s+10p≤100
  s+p≥5
• 4s+10p≤100
  p≥5
• s+p≤100
  4s+10p≥5
• 4+p≤10
  5+s≤100

Jonah is going to the store to buy candles. Small candles (s) cost $3.50 and large candles (L) cost $5.00. He needs to buy at least 20 candles, and he cannot spend more than $80. Write a system to represent the situation.

• 3.5s+5L≤80
  s+L≥20
• s+L≤80
  3.5s+5L≥20
• s+L>20
  3.5s+5L<80
• 8.5L≤80
  s+L≥20

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Eli is packing books into boxes. Each box can hold either 15 small books or 8 large books. He needs to pack at least 35 boxes and at least 350 books. Write a system using s and L to model this situation.

• 15s+8L>350
  s+L>35
• 15s+8L≤350
  s+L≤35
• s+L≥350
  15s+8L≥35
• s+L≥35
  15s+8L≥350

Suppose you have a job mowing lawns (x) that pays $12 per hour. You also have a job at a clothing store (y) that pays $10 per hour. You need to earn at least $350 per week, but you can work no more than 35h per week.

• 12x+10y≥350
  x+y≤35
• 12-x≥y
  350-y≤x
• 12x+10y≤35
  x+y≥350
• x+y≤35
  10x+12y≥350

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Two friends agree to split the driving on a road trip from Philadelphia to Denver. One friend (x) drives at an average speed of 60 mi/h. The other friend (y) drives at an average speed of 55 mi/h. They want to drive at least 500 mi per day. They plan to spend no more than 10h driving each day. How many hours could each friend drive?

• 55x+60y≥500
  x+y≤10
• x+y≥500
  60x+55y≤10
• x+y<10
  55x+60y>500
• x+y≤10
  60x+55y≥500

A salad contains ham and chicken. There are fewer than 6 pounds of ham and chicken in the salad. There's at least 1 pound of chicken in the salad. Write a system of inequalities to find how many pounds of each could be included.

• h+c<6
  c≥1
• h+c<6
  c>1
• h+c≤6
  c≥1
• 6-h≥c
  h≥1

Mary babysits for $4 an hour. She also works as a tutor for $7 an hour. She is only allowed to work 13 hours per week. She wants to make at least $65. Write a system to model this situation.

• b+t≥65
  4b+7t≤13
• b+t≥13
  4b+7t≤65
• b+t≤13
  4b+7t≥65
• 7b+4t≥65
  b+t<13