Application of Systems of Equations

The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior tickets and 5 student tickets. Which system of equation listed below could be used to solve the price of each senior and student ticket?

• 4c + 5s = 102

  7c + 5s = 126

• 7c + 5s = 102

  4c + 5s = 126

• 4c - 5s = 102

  7c - 5s = 126

• 7c - 5s = 102

  4c - 5s = 126

A hotel offers two activity packages. Package A costs $192 and includes 3 hours of horseback riding and 2 hours of parasailing. Package B costs $213 and includes 2 hours of horseback riding and 3 hours of parasailing. Which system of equations below could be used to solve for the price of each hour of horseback riding and parasailing?

• 3h + 3p = 192

  2h + 2p = 213

• 2h - 2p = 192

  3h - 3p = 213

• 3h - 2p = 192

  2h - 3p = 213

• 3h + 2p = 192

  2h + 3p = 213

Suppose you got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $14.50. Which system of equations below represents how you could find the cost of each mango and apple?

• 5m + 3a = 18

  3m + 8a = 14.50

• 5m + 8a = 18

  3m + 3a = 14.50

• 8m + 3a = 18

  3m + 5a = 14.50

• 8m + 5a = 18

  3m + 3a = 14.50

Kensington's talent show will feature 12 solo acts and 2 ensemble acts. The show will last 90 minutes. The 6 solo performers judged best will give a repeat performance at a second 60-minute show, which will also feature 2 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes. Which system of equations below could be solved to find the length of each act?

• 6x + 2y = 90

  12x + 2y = 60

• 6x - 2y = 90

  12x - 2y = 60

• 12x + 2y = 90

  6x + 2y = 60

• 12x - 2y = 90

  6x - 2y = 60

A student purchased 3 boxes of pencils, x, and 2 boxes of pens, y, for $6. He then purchased 2 boxes of pencils and 4 boxes of pens for $8. What is the cost of each box of pens?

• Each box of pens costs $1.

• Each box of pens costs $1.25.

• Each box of pens costs $1.50.

• Each box of pens costs $1.75.

At Whole Foods, you can purchase 3 pounds of raspberries and 5 pounds of strawberries for $42. You can purchase 5 pounds of raspberries and 3 pounds of strawberries for $38. Which system of equations below could be used to find out the price of each pound of raspberries and strawberries?

• 3r + 5s = 42

  5r + 3s = 38

• 3r - 5s = 42

  5r - 3s = 38

• 3r + 3s = 42

  5r + 5s = 38

• 5r + 5s = 42

  3r + 3s = 38

At Whole Foods, you can purchase 3 pounds of raspberries and 5 pounds of strawberries for $42. You can purchase 5 pounds of raspberries and 3 pounds of strawberries for $38. What is the price for each pound of strawberries?

• Each pound of strawberries costs $3.

• Each pound of strawberries costs $4.

• Each pound of strawberries costs $5.

• Each pound of strawberries costs $6.

The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior tickets and 5 student tickets. Which answer below shows the correct price of each senior citizen ticket and each student ticket?

• $8 for a senior ticket, $12 for a student ticket

• $8 for a senior ticket, $14 for a student ticket

• $12 for a senior ticket, $8 for a student ticket

• $14 for a senior ticket, $8 for a student ticket

Suppose you got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $14.50. What is the price of each mango and apple?

• $1.25 per mango, $2.25 per apple

• $1.50 per mango, $2 per apple

• $1.75 per mango, $1.75 per apple

• $2 per mango, $1.50 per apple

A toy store worker packed two boxes of identical dolls and plush toys for shipping. One box held 3 dolls and 4 plush toys, and the box weighed 27 ounces. Another box held 2 dolls and 3 plush toys and weighed 19 ounces. Which system of equations listed below can be used to find how many ounces each item weighs?

• 2x + 3y = 27

  3x + 4y = 19

• 3x + 4y = 27

  2x + 3y = 19

• 3x + 3y = 27

  2x + 4y = 19

• 2x + 4y = 27

  3x + 3y = 19