System of Equations Graphing Word Problems

Yazzy won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Yazzy have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49

• x + y = 49
  10x + 5y = 1430 

• x + y = 49
  20x + 50y = 1430

• x + y = 49
  x + y = 1430

On Monday Jay bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Dishann 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

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Cullin needs to save at least $100 for homecoming.  He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns.  He only has time to work 14 hours before homecoming. 

• x + y  ≥ 25
  x + y ≤ 8

• 100x + 25 y ≤ 100
  2x + 8y ≤ 14

• x + y ≥ 100
  8x + 25y ≤ 14

• 8x + 25y ≥ 100
  x + y ≤ 14

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. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91

• x + y = 91
  14.80x + 17y = 6

• x + y = 6
  14.80y + 17x = 91

• x + y = 91
  14.80x+ 17y = 6

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x

  y = 8.40 + x

• y = 9.65x + 43

  y = 8.40x + 58

• y =9.65x

  y = 8.40x

• y = 9.65x - 43

  y = 8.40x - 58

A system of equations is shown.

y = –5x – 2

y = 3x – 4

What is the solution to the system of equations?

• (¹/₄, -¹³/₄)

• (¹/₄, -³/₄)

• (4,-22)

• (4,8)

Jane and Chris sell candles to earn money. Jane spent $20 to create her candles and sells candles for $3 each. Chris spent $40 to create his candles and sells candles for $5 each. How many candles will Jane and Chris have to sell in order to earn the same profit?

Maggie has $15.00 and will begin earning an allowance of $10.00 per week. Jess has $5.00 and will begin earning an allowance of $15.00 per week. When will Maggie and Jess have the same amount of money and how much money will they each have?

• After 2 weeks, they will each have $60.00.

• After 2 weeks, they will each have $35.00.

• After 4 weeks, they will each have $60.00.

• After 4 weeks, they will each have $35.00.