Solutions for Linear Word Problems

1) A plumber charges $25 for a service call plus $50 per hour of service. What information is given and what equation should you use?

• A slope and a y - intercept are given; use y = mx + b.

• A slope and a y - intercept are given; use y - y1 = m(x - x1).

• Two points are given; find m and use y - y1 = m(x - x1).

• Two different rates (slopes) and a total are given; use Ax + By = C

For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. What information is given and what equation should you use?

• A slope and a y - intercept is given; use y = mx + b.

• A slope and a y - intercept is given; use y - y1 = m(x - x1).

• Two points are given; use y - y1 = m(x - x1).

• Two different rates (slopes) and a total are given; use Ax + By = C

You took a standardized test on which all of the questions had to be answered. Your received 2 points for each correct answer but lost ½ point for each incorrect answer. Your score was 85 points. What information is given and what equation should you use?

• A slope and a y - intercept is given; use y = mx + b.

• A slope and a y - intercept is given; use y - y1 = m(x - x1).

• Two points are given; find m and use y - y1 = m(x - x1).

• Two different rates (slopes) and a total are given; use Ax + By = C

Mr. P goes to the comic book store and purchases issues of Justice League and X - Men. Justice league comics are priced at $4.99 each, and X - Men comics are priced at $3.99 each. He spent $36.92. What information is given and which equation should you use?

• A slope and y - intercept are given; use y = mx + b.

• A slope and y - intercept are given; use y - y1 = m(x - x1).

• Two points are given; find m and use y - y1 = m(x - x1).

• Two different rates (slopes) and a total are given; use Ax + By = C

When 4 people attend the movie theater, it costs $23.96. When 7 people attend the movie theater, it costs $41.93. What information is given and which equation should you use?

• A slope and y - intercept are given, use y = mx + b.

• A slope and y - intercept are given, use y - y1 = m(x - x1).

• Two points are given; use y - y1 = m(x - x1).

• Two different rates (slopes) and a total are given; use Ax + By = C

When an individual rides in a taxi for 20 miles, it costs them $21. Another individual rides in the same taxi for 30 miles and pays $26.50. What information is given and which equation should you use?

• A slope and y - intercept is given; use y = mx + b.

• A slope and y - intercept is given; use y - y1 = m(x - x1).

• Two points are given; find m and use y - y1 = m(x - x1).

• Two different rates (slopes) and a total are given; use Ax + By = C

You and your friends go to the movies and purchase some popcorn and Pepsi. Popcorn is sold for $4.99 per bag and Pepsi is sold for $1.99 per bottle. You each chip in to pay $24.92. Write an equation to represent the given situation.

• y = 1.99x + 4.99

• y = 4.99x + 24.92

• y - 1.99 = 4.99(x - 24.92)

• 1.99x + 4.99y = 24.92

Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation to represent the given situation.

• y = -0.5x + 34

• y = -34x + 0.5

• y - 34 = 0.5(x - 1)

• 34x - 0.5y = 33.5

1) A plumber charges $25 for a service call plus $50 per hour of service. Write an equation for the given situation.

• y = 50x + 25

• y = 25x + 50

• y - 50 = 1(x - 25)

• 25x + 50y = 75

1) A caterer charges $100 to cater a party for 10 people and $175 for 25 people. Write an equation for the given situation.

• y = 25x + 100

• y - 100 = 5(x - 10)

• y - 175 = 10(x - 25)

• 100x + 175y = 35