Formulate 3 Variable Systems

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

AII.9-12.3.A

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80
• d + n = 80
  d + n = 6.60
• d + n = 80
  .10d + .05n = 6.60
• d + n = 80
  .05d + .10n = 6.60

Tags

AII.9-12.3.A

The perimeter of rectangular box is 18 inches and the width is five inches less than the length. If W=width of the box and L=length of the box, which system of equations matches the situation?

• L + W = 18
  W = L - 5
• 2L + 2W = 18
  L = W - 5
• 2L + 2W = 18
  W = L - 5
• 2L + 2W = 18
  W = 5 - L

Tags

AII.9-12.3.A

Erica has $14 and plans to save $5 each week until she has the $64 she needs for a new jacket. How many weeks will it take Erica to save money for a new jacket? Use w as the number of weeks.

• 5 + 14w = 64

• 14 + 5w = 64

• 19w = 64

• 5w - 14 = 64

Tags

AII.9-12.3.A

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

AII.9-12.3.A

Two numbers have a sum of 25.

One number is five more than the other number. Find the numbers.

Which system best represents the information?

• x + y = 25

  x = 5 + y

• xy = 25

  x = 5 + y

• x + y = 25

  x = 5y

• xy = 25

  x = 5y

Tags

AII.9-12.3.A

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

AII.9-12.3.A

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

AII.9-12.3.A

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

AII.9-12.3.A

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?

• 
  

  $m\ +\ c\ +\ v\ =\ 180$

  $v\ =\ m\ +\ 5$
  $c\ =\ 3\left(m\ +\ v\right)$
  

• $m\ +\ c\ +\ v\ =\ 180$
  $m\ =\ v+5$
  $c\ =\ 3m\ +\ v$
  

• $c\ +\ m\ +\ v\ =\ 180$
  $m\ =\ v+5$
  $3c\ =\ m+v$
  

Tags

AII.9-12.3.A