System of Equations Real World Problems

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530

  3S + 4A = 1740

• S + A = 530

  4S + 3A = 1740

• S + A = 1740

  3S + 4A = 530

• S + A = 1740

  4S + 3A = 530

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? (Let x represent chicken dinners and y represent steak.)

• x + y = 6

  14.80x + 17y = 91

• x + y = 91

  14.80x + 17y = 6

• x + y = 6

  14.80y + 17x = 91

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales. Which system best represents the situation?

• 4m + 7r = 578

  m + r = 3365

• 4m + 7r = 3365

  m + r = 578

• 4m + 7r = 578

  m + r = 3365

• 4r + 7m= 3365

  m + r = 578

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 customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Eastern View is selling tickets for their fall musical. On the first day of sales, we sold 3 adult tickets and 9 student tickets. They made $75. On the second day of sales, we sold 8 adult tickets and 5 student tickets and made $67. How much does an adult and a student ticket cost?

• An adult ticket costs $4 and a student ticket costs $7.

• An adult ticket costs $7 and a student ticket costs $4.

• An adult ticket costs $6 and a student ticket costs $3.

• An adult ticket costs $3 and a student ticket costs $6.

Click on the picture for the question

• A

• B

• C

• D

Write a system of equations to describe the situation and solve. A TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 5 sitcoms and 2 dramas, for a total of 199 minutes of shows. On Tuesday nights, he has scheduled 3 sitcoms and 5 dramas, for a total of 298 minutes of shows. All sitcoms have the same length and all dramas have the same length. How long is each type of show?

• 22 minutes for a sitcom and 46 minutes for a drama

• 23 minutes for a sitcom and 47 minutes for a drama

• 22 minutes for a sitcom and 45 minutes for a drama

• 21 minutes for a sitcom and 47 minutes for a drama

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation