Real World Application System of Equations

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

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. What is the cost of one hour of each activity?

• $20 for horseback riding, $61 for parasailing

• $25 for horseback riding, $56 for parasailing

• $30 for horseback riding, $51 for parasailing

• $35 for horseback riding, $46 for parasailing

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

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

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. How much does each doll weigh?

• Each doll weighs 3 ounces.

• Each doll weighs 4 ounces.

• Each doll weighs 5 ounces.

• Each doll weighs 6 ounces.

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. Which system of equations below could be used to find the cost of each box of pencils and pens?

• 2x + 2y = 6

  3x + 4y = 8

• 3x + 2y = 6

  2x + 4y = 8

• 3x + 4y = 6

  2x + 2y = 8

• 4x + 2y = 6

  2x + 3y = 8

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.

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. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52