Lesson 19 Formulating a System of Equations

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450
• 3x + 2y = 450
  2x + 4y = 315
• 2x + 2y = 315
  3x + 4y = 450

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

The sum of three numbers is 35. The product of the first number times the third number is 87. The quotient of the third number divided by the first number is 1.5. Which of the following systems of equations can be used to determine the three numbers?

• x+y+z=35

  xz=87

  x-1.5z=0

• x+y+z=35

  xz=87

  -1.5x+z=0

• x+y+z=35

  xz=87

  x/z=1.5

• x+y+z=35

  xz=87

  1.5/x=z

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Simone has discovered a blow-out sale in the mall. The cost of 1 sweater, 3 shirts, and 2 pairs of pants is $100. The cost of 3 sweaters and 6 pairs of pants is $201. The cost of 8 shirts and 2 pairs of pants is $144. If x is the number of sweaters, y is the number of shirts, and z is the number of pants, which system of equations can be used to determine the sale price of the sweaters, shirts, and pants?

• x+3y+2z=100

  3x+6z=201

  8y+2z=144

• x+3y+2z=100

  3x+y+6z=201

  x+8y+2z=144

• x+y+z=172

  x+z=269

  y+z=74

• x+3y+2z=100

  3x-6z=201

  8y-2z=144

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

Choose the correct equations for the scenario.

A parking lot has spaces reserved for motorcycles, cars, and vans. There are five more spaces reserved for vans than for motorcycles. There are three times as many car spaces as van and motorcycle spaces combined. If the parking lot has 180 total reserved spaces, how many of each type are there?

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

Choose the correct variables for the scenario.

A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of student tickets, how many of each type of ticket were sold for the showing?

• a = number of adult tickets

  s = number of student tickets

  c = number of children tickets

• a = cost of 6 adult tickets

  s = cost of 3.5 student tickets

  c = cost of 2.5 children tickets

• a = cost of 1 adult tickets

  s = cost of 1 student tickets

  c = cost of 1 children tickets

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

Choose the correct equations for the scenario.

A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of student tickets, how many of each type of ticket were sold for the showing?

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1

Choose the correct variables for the scenario.

Sarah buys 1 lb. of jelly beans and 2 lb. of chocolates for $2.00. She then buys 1 lb. of jelly beans and 2 lb. of licorice for $3.00. She also buys 2lb. of chocolates and 2 lb. of licorice for $2.00. How much will it cost to buy 1lb. of each of the three candies?

• j = number of jellybeans

  c = number of chocolates

  l =number of licorice

• j = cost per 1 lb. of jellybeans

  c = cost per 1 lb. of chocolates

  l =cost per 1 lb. of licorice

• j = cost of 1 jellybean

  c = cost of 1 chocolate

  l =cost of 1 licorice

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1

Choose the correct equations for the scenario.

Sarah buys 1 lb. of jelly beans and 2 lb. of chocolates for $2.00. She then buys 1 lb. of jelly beans and 2 lb. of licorice for $3.00. She also buys 2lb. of chocolates and 2 lb. of licorice for $2.00. How much will it cost to buy 1lb. of each of the three candies?

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

Choose the correct variables.

A parking lot has spaces reserved for motorcycles, cars, and vans. There are five more spaces reserved for vans than for motorcycles. There are three times as many car spaces as van and motorcycle spaces combined. If the parking lot has 180 total reserved spaces, how many of each type are there?

• m = Cost of 1 motorcycle

  c = Cost of 1 car

  v = Cost of 1 van

• m =number of motorcycles

  c = number of cars

  v = number of van

• m =how many spaces for motorcycles

  c = how many spaces for cars

  v = how many spaces for van

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1