Linear Equations Word Problems
Example 4:
A company has fixed operating costs of $1,969.00 per month with a production cost of $14.98 per unit. If each
unit brings $28.30 in revenue, write an equation that represents the profit for the month. Let x represent the
number of units made and y represent the total profit for the month.
Example 5:
Sheila’s job has a base monthly salary of $1,400. For every sale she makes, she earns $30. If Sheila’s goal is to
earn $3,380 this month, how many sales does she need to make?
Example 6:
Forrest Lumber uses the function, S(t) = -75t + 600, to determine the salvage value, S(t), in dollars, of a table
saw t years after its purchase. How long will it take the saw to depreciate completely?
Example 7:
Marcus works as a salesman at a car dealership. He is paid a base salary of $1,309.62 each month, and he
receives a commission of $108.24 for each vehicle he sells. If last month Marcus earned $2,608.50, how many
cars did he sell last month?
Example 8:
Mike discovered that the pool in his backyard is leaking slowly. The pool holds 14,575 gallons of water, and is
leaking at a rate of 8 gallons per day. If Mike does not replace the water that has leaked from the pool, how
many gallons of water will remain in the pool after 106 days?
Example 9:
The staff at Larry’s Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an
average of twelve hours per day. The mowing and raking typically takes eight hours and an average of eighty
bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill
one bag of leaves?
Example 10:
Kirk pays $100 per month toward his school loan. He already paid $10,000. If the total loan amount is
$12,300, and no interest is figured into the calculation, how many more months will it take him to finish
paying the loan?
Example 11:
Erica went shopping for new clothes for school. She bought a pair of jeans for $50.15 and several shirts for
$9.85 each. If x represents the number of shirts she bought, write an equation to find y, the total cost of
Erica’s shopping trip.
Example 12:
Zach and his friends had a movie marathon on Saturday. Each movie they watched was two hours long. Five
hours into their movie marathon, Zach and his friends had watched 2.5 movies. Write an equation that
expresses the number of movies they watched, y, as a function of the number of hours they spent watching
movies.
Example 13:
The senior class officers have figured out that prom will cost $4,000 for location rental and decorations, and
another $47 per person for food. (a) Write an equation in general form that expresses the cost of prom in
dollars, y, as a function of the number of people who attend, x. (b) Use the equation you found to find the
total cost of prom if 120 people attend.
Example 14:
A company manufactures and sells mini recorders. A survey of office supply stores indicated that the demand
for 3 hundred recorders would cause them to be sold if they cost $98 each, and the demand for 13 hundred
recorders would cause them all to be sold if they cost $38 each. If a linear relationship between demand and
price exists, write an equation to model the demand-price relationship. (Let x represent the demand in
hundreds and y represent the price to mini recorder.)
Example 15:
The Bridgeport water department has a monthly service charge of $15.30 and a volume charge of $1.91 for
every 100 cubic feet of water. Write an equation that can be used to determine the Morgan family’s monthly
water bill. (Let x represent 100 cubic feet of water and y represent the monthly cost.)
Example 16:
Dilbert’s TV and Appliance discounts all televisions 9% to customers paying in cash. Rebecca paid $1,723.53 in
cash and before tax for a 52-inch widescreen TV. What was the original price of the TV not including tax?
Example 17:
Reid’s Hardware discounts all riding lawnmowers 8% to customers paying in cash. If Trey paid $1,153.69 in
cash for a riding lawnmower, write an equation that can be used to determine the original price of the
lawnmower.