System of Linear Equations Word Problem Area Perimeter

The perimeter of a rectangular wooden deck is 90 feet. The deck's length, l, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck?

• 2l + 2w = 90
  l = 5 - 4w
• 2l + 2w = 90
  l = 4 - 5w
• 2l + 2w = 90
  l = 5w = 4
• 2l + 2w = 90
  l = 4w - 5

Kalya rides her bicycle at an average speed of 10 miles per hour. One day she rode her bicycle for b hours and walked for w hours, and traveled a total of 24 miles. The entire trip took 4.5 hours. Based on her average speeds for riding and walking, which of these systems of equations could be used to determine b and w?

• b + w = 24
  10b + 3w = 4.5
• b + w = 4.5
  10b + 3w = 24
• b + w = 24
  3b + 10w = 4.5
• b + w = 4/5
  3b + 10w = 24

Last week Angela went grocery shopping and bought 3 boxes of Crunchy O's cereal and 2 gallons of milk for at total of $16.65. This week at the same prices, she bought 2 boxes of the same Crunchy O's cereal and 1 gallon of milk for $9.77. Which system of equations can be used to find c, the cost of a box of cereal, and m, the cost of a gallon of milk?

• 3c + 2m = 16.65
  2c + m = 9.77
• 2c + 3m = 16.65
  c + 2m = 9.77
• 3c + 2m = 9.77
  2c + m = 16.65
• 3c + 2m = 16.65
  2c + 2m = 9.77

The Rodriguez family ordered pizzas for a party. A large pizza costs $4.25 more than a medium pizza. They bought 4 large and 6 medium pizzas, and the total cost without tax was $99.50. Which pair of equations can be used to find the cost of a large pizza, L, and the cost of a medium pizza, M?

• L = M - 4.25
  4L + 6M = 99.50
• L = 4.25 + M
  6L + 4M = 99.50
• L = 4.25 - M
  4L + 6M = 99.50
• L = 4.25 + M
  4L + 6M = 99.50

Anna counts her coins and finds that she has 55 coins with a total value of $9.25. If all of the coins are either quarters or dimes, which system of equations can be used to calculate the number of (d) and quarters (q) that Anna has?

• 0.25q + 0.10d = 9.25
  q + d = 55
• 0.25d + 0.10q = 9.25
  q + d = 55
• 0.25q + 0.10d = 55
  q + d = 9.25
• 0.25q = 0.10d - 55
  q + d = 55

Let x and y be two supplementary angels, where the measure of x is three times the measure of y. Which system of equations below could be used to find the measures of the two angles?

• x + y = 180
  x = y + 3
• x + y = 180
  y = x + 3
• x + y = 180
  y = 3x
• x + y = 180
  x = 3y

Alicia mailed postcards (p) and letters (l) to her friends while she was on vacation. She spent a total of $9.00 on postage to mail a total of 40 pieces of mail. She spent $0.35 on each letter and $0.15 on each postcard. Which system of equations could you set up to find out how many postcards and how many letters she mailed?

• p + l = 9
  0.35p + 0.15l = 40
• p + l = 40
  0.35p + 0.15l = 9
• p + l = 9
  0.15p + 0.35l = 40
• p + l = 40
  0.15p + 0.35l = 9

At the flea market, Mr. Rhodes sells handmade shirts for $15 and baseball hats for $12. This past weekend, Mr. Rhodes sold 14 more shirts than hats and made $480 in sales. Which systems of equations can be used to find s, the number of shirts, and h, the number of hats Mr. Rhodes sold this past weekend?

• 15h + 12s = 480
  h = s + 14
• 15s + 12h = 480
  s = h + 14
• 15s + 12h = 480
  s = h - 14
• 15s + 12h = 14
  s + h = 480

Narissa wants to put a wooden border around the edge of her rectangular dining room floor. She knows the perimeter of the dining room is 64 feet and that the dining room's length is 4 feet less than its width. Which system of equations can Narissa use to determine the length, l, and the width, w, of the dining room in feet?

• l + w = 64
  l = w - 4
• 2l + 2w = 64
  l = w + 4
• 2l + 2w = 64
  l + w = 4
• 2l + 2w = 64
  l + 4 = w

It costs $1.50 for children and $2.00 for adults to ride the Ferris wheel at the county fair. On Saturday, the Ferris wheel operator collected money from 700 people. If he collected a total of $1,170, which system of linear equations could be used to find a, the number of adults, and c, the number of children that rode the Ferris wheel on Saturday?

• c + a = 700
  1.5c + 2a = 1,170
• c + a = 1,170
  2c + 4.5a = 700
• c + a = 700
  2c + 1.5a = 1,170
• c + a = 1,170
  1.5c + 2a = 700