Slope Intercept Word Problems

1.  The base pay of a water delivery person is $210 per week. He also earns 20% commission on each sale he makes.

  1. Write an equation that relates the total earnings “t” to sales “s”.
  1. How much would he earn if he sells $250 worth of merchandise?

2.  A music store is offering a coupon promotion on its CDs. The regular price for CDs is $14. With the coupon, customers are given $4 off the total purchase.

  1. Write an equation that relates the number of CDs “c” and the total cost “t”.
  1. Find the total cost for a sale of 6 CDs.

3.  Suppose you have $55 in your bank account. You start saving $10 each week.

  1. Write an equation that relates the number of weeks “w” to the amount of money you have in your account “a”
  1. How much money will you have in your account in 7 weeks?

4.  A communications company offers a variety of calling card options. Card A has a 30 cent connection fee and then costs 2 cents per minute.

  1. Write an equation that relates the number of minutes “n” to the cost of the call “c”
  1. How long could you talk for $15.10?

5.  You are testing fertilizers on plants. One plant is 11 cm tall and growing at a rate of 1 cm/day.

  1. Write an equation that relate the number of days “d” to the height of the plant “h”
  1. How many days will have passed when the plant is 65 cm tall?


Point Slope Word Problems

1.  At the surface of the ocean, pressure is 1 atmosphere. At 66 feet below seal level, the pressure is 3 atmospheres. The relationship of pressure and depth is linear.

  1. Write an equation for the data in point-slope form.
  1. Re-write the equation in slope-intercept form.
  1. Predict the pressure at 100 feet below seal level.

2.  The relationship between the altitude and the boiling point of water is linear. Water boils at 197.6 oF when it is 8000 feet above sea level and at 207.5 oF when it is 2500 feet above sea level.

  1. Write an equation for the data in point-slope form.
  1. Re-write the equation in slope-intercept form.
  1. Predict the boiling temperature of water when it is 4500 feet above sea level.

3.  Lydia is adding $5 to her savings account every week. After 2 weeks she has $64 in her account.

  1. Write an equation for the data in point-slope form.
  1. Rewrite the equation in slope-intercept form.
  1. What does the y-intercept mean in this problem?
  1. How much will Lydia have saved after a year?

4.  In the 1988 Olympics, the women’s winning long jump was about 24.7 feet. It is predicted that by 2020 the record will be about 26.3 feet.

  1. Write the point-slope form of an equation for the information.
  1. How far do you predict the winning long jump will be in 2050?

5.  The Pacific giant kelp plant grows at a rate of 45 centimeters per day. On the second day of its growth the plant is 90 centimeters long.

  1. Write the point-slope form of an equation for the data.
  1. How much growth will the kelp plant have after 5 weeks?


Standard Form Word Problems

1.  You are sent to the store to buy sliced meat for a party. You are told to get rosast beef and turkey, and you are given $30. Roast beef is $4.29/lb and turkey is $3.99/lb.

  1. Write an equation in standard form to relate the pounds of each kind of meat you could buy at the store with $30.
  1. Find 3 possible options for the amount of beef and turkey bought.

2.  Suppose your school is having a talent show to raise money for new music supplies. You estimate that 200 students and 150 adults will attend. You estimate $200 in expenses.

  1. Write an equation to find what ticket prices you should set to raise $1000.
  1. Find 3 possible options for the cost of adult and student tickets

3.  Larry runs at an average rate of 8 mi/h. He walks at an average rate of 3 mi/h.

  1. Write an equation in standard form to relate the times he could spend running and walking if he travels a distance of 15 miles.
  1. Find 3 possible options for the time spent running and walking.

4.  Your younger brother’s elementary school class sells a different brand of gift wrap, which costs $2 per package, and cards, which cost $5 per package.

  1. Write an equation in standard form to find what how many rolls of gift wrap and how many cards you must sell to raise $150.
  1. Find 3 possible options for how many rolls of gift wrap and how many cards.

5.  An order of 3 burritos and 4 tacos costs $11.33.

  1. Write an equation in standard form for the cost of a burrito and a taco.
  1. Find 3 possible options for how much a burrito and a taco could cost.


Various Linear Equations Word Problems.

For each of the problems below:

a.  Determine the best form to use (slope-intercept, standard, point-slope).

b.  Set up an equation using one of the three forms of linear equations we have learned this unit.

c.  Convert each equation to slope intercept form.

1.  A tri-athlete covers 60 miles every day. He runs at a rate of 8.5 miles per hour and rides his bike at a rate of 27 miles per hour.

2.  A job at a retail store pays $75 each week plus 25% commission on total weekly sales.

3.  A kitten grows from 5 oz. at birth to 3lb 5 oz. at 6 months. (Hint: 1 lb. = 16 oz.)

4.  Five one-subject notebooks and 3 two-inch binders cost $17.50 at Staples.

5.  A baby elephant is born weighing 212 pounds and gains 30 pounds a month for the first 5 years of his life.