Solving System of Equations Word Problems

Last season two running backs on the Steelers football team rushed a combined (both running backs) 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

Tags

CCSS.8.EE.C.8C

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 (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

Tags

CCSS.8.EE.C.8C

On Monday Joe bought 10 cups of Coffee and 5 Doughnuts for his office at the (total) 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

Tags

CCSS.8.EE.C.8C

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos

  m: # of glasses of milk

• t: Cost of each taco

  m: Cost of each glass of milk

• t: total cost

  m: # of food items

Tags

CCSS.8.EE.C.8C

Some students want to order shirts with their school logo. One company charges a total of $9.65 per shirt plus a setup fee of $43. Another company charges a total of $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

Tags

CCSS.8.EE.C.8C

Lisa and Tammy are selling items at the craft show. Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount? (Where will the two lines touch?)

• (1, 12)

• (3, 19)

• (5, 25)

Tags

CCSS.8.EE.C.8B

The equations of two lines are 6x + y = 26 and y = 2x + 10. If the solution is (2, y), what is the value of y? (Hint: 1st solve the 1st equations for y, 2nd graph both equations, 3rd determine where the two lines touch. After solving, use menu 3, 2 on the N-Spire, or use the DESMOS calculator.)

• 14

• 4

• 6

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. How many of each type of ticket were sold?

• 10 adults, 11 children

• 12 adults , 9 children

• 11 adults, 10 children

• 9 adults, 12 children

Tags

CCSS.8.EE.C.8C

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5

• $10

• $15

• $20

Tags

CCSS.8.EE.C.8C

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x

• The  y

• The  z

• The unknown

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6