Writing Systems of Equations from Word Problems

Michael spent $50 for 6 tigerfish and 8 goldfish. Shaun spend $5 more than Michael for 5 tigerfish and 10 goldfish. Write a system of equations that could be use the find t, the price of a tigerfish and g, the price of a goldfish.

• $8t+6g=50$
  $10t+5g=55$
  

• $6t+8g=50$
  $5t+10g=45$
  

• $6t+8g=50$
  $5t+10g=55$
  

• $8t+6g=50$
  $10t+5g=45$
  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Sarah enjoys cutting lawns and charges $20 for each small lawn and $30 for each large lawn she mows. Sarah earned $140 for mowing 6 lawns. Write a system of equations that could be used to find x, small lawns and y, large lawns Sarah mowed.

• $30x+20y=140$
  $x+y=6$
  

• $50\left(x+y\right)=140$
  $x+y=6$
  

• $20x+30y=140$
  $x+y=6$
  

• $x+y=140$
  $x+y=6$
  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

The length of a rectangular playground is 4 meters less than 3 times the width. The perimeter is 64 meters. Write a system of equations that could be used to find l, the length and w, the width of the rectangular playground.

• $l=3w-4$
  $2l+2w=64$
  

• $l=3w-4$
  $l+w=64$
  

• $l=4-3w$
  $2l+2w=64$
  

• $l=4-3w$
  $l+w=64$
  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

The drama club is selling tickets to its play. The cost of an adult ticket is $4.50, and the cost of a student ticket is $2.50. The theater can hold 250 people and they want to make $1,005. Write a system of equations that could be used to find x, the number of adult tickets and y, the number of student tickets.

• $4.50x+2.50y=1,005$
  $x+y=250$
  

• $4.50x+2.50y=250$
  $x+y=1,005$
  

• $2.50x+4.50y=1,005$
  $x+y=250$
  

• $2.50x+4.50y=250$
  $x+y=1,005$
  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

Kacey is thinking of two numbers. Their sum is -18. Their difference is 38. Write a system of equations that could be used to find the two numbers.

• $x+y=-18$
  $x-y=38$
  

• $x-y=-18$
  $x+y=38$
  

• $x\cdot y=-18$
  $x\div y=38$
  

• $x\div y=-18$
  $x\cdot y=38$
  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

The Spanish Club is selling tacos for a fundraiser. One student sold 12 chicken tacos and 15 beef tacos and raised $61.23. Another student raised $13.45 more than the first student by selling 10 chicken tacos and 22 beef tacos. Write a system of equations that could be used to find c, the price of chicken tacos and b, the price of beef tacos sold in the fundraiser.

• $12c+15b=61.23$
  $10c+22b=47.78$
  

• $12c+15b=61.23$
  $10c+22b=74.68$
  

• $15b+12c=61.23$
  $22c+10b=74.68$
  

• $15b+12c=61.23$
  $22c+10b=47.78$
  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings (x) when both companies cost (y) the same amount?

• y = 6.80 + .65x

  y=7.30+.90x

• x + y = 6.80

  x + y = 7.30

• y = 6.80+.90x

  y = 7.30 + .65x

• y + .90x = 6.80

  y + .65x = 7.30

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables? 

• t: # of tacos
  m: # of glasses of milk
• t: Cost of each taco
  m: Cost of each glass of milk
• t: total cost
  m: # of food items
• t: Cost of each glass of milk
  m: Cost of each taco

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations best represents the situation?

• h + c = 15

  4h + 2c = 44

• 4h + 2c= 15

  h + c = 44

• h = 2c + 44

  4h = c + 15

• 2h - 4c = 44

  h - c = 15

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530

  3S + 4A = 1740

• S + A = 530

  4S + 3A = 1740

• S + A = 1740

  3S + 4A = 530

• S + A = 1740

  4S + 3A = 530

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6