Systems of Equations Word Problems

Find the value of two numbers if their sum is 12 and their difference is 4.

• The numbers are 8 and 4

• The numbers are 10 and 2

• The numbers are 9 and 3

• The numbers are 7 and 5

Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Write a system of equations to represent this situation. How many adult tickets and student tickets were purchased?

• Adult ticket: $5, Student ticket: $3

• Adult ticket: $12, Student ticket: $6

• Adult ticket: $8, Student ticket: $14

• Adult: $15, Student ticket: $5

The difference of two numbers is 3. Their sum is 13. Find the numbers.

• 5 and 8

• 6 and 9

• 4 and 7

• 7 and 10

Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.

• Wind speed: 23 km/h, Plane speed: 135 km/h

• Wind speed: 20 km/h, Plane speed: 138 km/h

• Wind speed: 23 km/h, Plane speed: 138 km/h

• Wind speed: 20 km/h, Plane speed: 135 km/h

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38.00. The school took in $52.00 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

• Senior citizen ticket: $10, Child ticket: $8

• Senior citizen ticket: $12, Child ticket: $6

• Senior citizen ticket: $8, Child ticket: $14

• Senior citizen ticket: $15, Child ticket: $5

Concession: You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. Write the system equations for the number of hot dogs and sodas sold.

• h + s = 78.50

  1.50h + 0.50s = 87

• h + s = 87

  1.50h + 0.50 = 78.50

• h + s = 87

  0.50h + 1.50s = 78.50

• h + s = 78.50

  0.50h + 1.50s = 87