Systems of Equations Word Problems and Inequalities

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If E=Erin's age and A=Alex's age, choose the system that matches the situation.

• E + A = 33

  A = 2E - 3

• E + A = 33

  E = 2A - 3

• E + A = 33

  E = 3 - 2A

• E + A = 3

  E = 33 - 2A

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Where h=horses and c=chickens. Which system of equations 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

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Where a=apples and b=bananas. Which system of equations represents the situation?

• 4a + 6b = 3

  13.50a - 13b = 6

• a + b = 4

  a - b = 6

• 4a + 6b = 13

  3a + 7b = 13.50

• 4a - 6b = 13

  3a - 7b = 13.50

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. The total receipts were $1740. Where S=Student tickets and A=Adult tickets. 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

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

• x + y = 1550

  y = 4x

• x + y = 1550

  y = x + 4

• y - x = 1550

  y = 4x

• y = 1550 + x

  y = x + 4

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Let x and y represent the two numbers. Which system of equations represents the situation?

• x - y = -10

  x + y = -2

• x = -2

  y = 5

• x + y = -2

  x - y = -10

• x + y = -10

  x - y = -2

Tags

CCSS.HSA.CED.A.3

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8
• t + n = 54
  n = 3t + 8
• t + n = 54
  t = 3n - 8
• t + n = 8
  t = 3n + 54

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. The total bill was $91. Where c=chicken dinners ordered and s=steak dinners ordered. Which system best represents the situation?

• c + s = 6

  14.80c + 17s = 91

• c + s = 91

  14.80c + 17s = 6

• c + s = 6

  14.80c + 17s = 91

• c + s = 91

  14.80c+ 17s = 6

Which system of inequalities is shown?

• y ≥ -x - 1

  y < x + 4

• y < -x - 1

  y≤ x + 4

• y > -x - 1

  y ≥ x + 4

• y > -x + 1

  y ≥ x + 4

Is (-2,4) a solution to the system?

• Solution
• Not a solution