Name the two unknowns, then find the two facts the story gives about them: usually one counts things and one adds up their values. Each fact is one equation.
Plan A costs $125 up front and $31 a month. Plan B costs $50 up front and $56 a month. After how many months do they cost the same, and what is that cost?
A plane goes 850 miles with the wind in 2 hours and 1675 miles against the wind in 5 hours. Find its speed in still air and the speed of the wind.
Coffee at $1.50 a pound is mixed with coffee at $5.00 a pound to make 14 pounds of a blend worth $2.25 a pound. How many pounds of each?
Plan A costs $60 up front and $24 a month. Plan B costs $30 up front and $29 a month. After how many months do they cost the same, and what is that cost?
A boat goes 30 miles downstream in 1 hour and 66 miles upstream in 3 hours. Find its speed in still water and the speed of the current.
Coffee at $2.50 a pound is mixed with coffee at $7.50 a pound to make 20 pounds of a blend worth $6.25 a pound. How many pounds of each?
Plan A costs $310 up front and $25 a month. Plan B costs $10 up front and $45 a month. After how many months do they cost the same, and what is that cost?
A plane goes 340 miles with the wind in 1 hour and 1200 miles against the wind in 4 hours. Find its speed in still air and the speed of the wind.
How many pounds of $3.50 coffee must be mixed with 2 pounds of $8.00 coffee to make a blend worth $5.00 a pound?
The sum of two numbers is 123 and their difference is 39. Find the two numbers.
A boat goes 81 miles downstream in 3 hours and 126 miles upstream in 6 hours. Find its speed in still water and the speed of the current.
Coffee at $1.00 a pound is mixed with coffee at $8.00 a pound to make 14 pounds of a blend worth $5.50 a pound. How many pounds of each?
A jar holds 44 coins, all dimes and quarters, worth $8.60. How many of each are there?
A boat goes 92 miles downstream in 4 hours and 133 miles upstream in 7 hours. Find its speed in still water and the speed of the current.
Coffee at $1.50 a pound is mixed with coffee at $7.50 a pound to make 34 pounds of a blend worth $4.50 a pound. How many pounds of each?
Adult tickets cost $9 and child tickets $5. A total of 86 tickets were sold for $642. How many of each were sold?
A boat goes 96 miles downstream in 4 hours and 48 miles upstream in 6 hours. Find its speed in still water and the speed of the current.
How many pounds of $1.50 coffee must be mixed with 2 pounds of $5.50 coffee to make a blend worth $3.10 a pound?
The sum of two numbers is 35 and their difference is 23. Find the two numbers.
A boat goes 72 miles downstream in 3 hours and 40 miles upstream in 5 hours. Find its speed in still water and the speed of the current.
Systems of Equations Word ProblemsAnswer keyVersion 1
Date Period
Write a system of equations and solve it.
Plan A costs $125 up front and $31 a month. Plan B costs $50 up front and $56 a month. After how many months do they cost the same, and what is that cost?3 months, $218
A plane goes 850 miles with the wind in 2 hours and 1675 miles against the wind in 5 hours. Find its speed in still air and the speed of the wind.plane 380 mph, wind 45 mph
Coffee at $1.50 a pound is mixed with coffee at $5.00 a pound to make 14 pounds of a blend worth $2.25 a pound. How many pounds of each?11 lb at $1.50, 3 lb at $5.00
Plan A costs $60 up front and $24 a month. Plan B costs $30 up front and $29 a month. After how many months do they cost the same, and what is that cost?6 months, $204
A boat goes 30 miles downstream in 1 hour and 66 miles upstream in 3 hours. Find its speed in still water and the speed of the current.boat 26 mph, current 4 mph
Coffee at $2.50 a pound is mixed with coffee at $7.50 a pound to make 20 pounds of a blend worth $6.25 a pound. How many pounds of each?5 lb at $2.50, 15 lb at $7.50
Plan A costs $310 up front and $25 a month. Plan B costs $10 up front and $45 a month. After how many months do they cost the same, and what is that cost?15 months, $685
A plane goes 340 miles with the wind in 1 hour and 1200 miles against the wind in 4 hours. Find its speed in still air and the speed of the wind.plane 320 mph, wind 20 mph
How many pounds of $3.50 coffee must be mixed with 2 pounds of $8.00 coffee to make a blend worth $5.00 a pound?4 lb
The sum of two numbers is 123 and their difference is 39. Find the two numbers.81 and 42
A boat goes 81 miles downstream in 3 hours and 126 miles upstream in 6 hours. Find its speed in still water and the speed of the current.boat 24 mph, current 3 mph
Coffee at $1.00 a pound is mixed with coffee at $8.00 a pound to make 14 pounds of a blend worth $5.50 a pound. How many pounds of each?5 lb at $1.00, 9 lb at $8.00
A jar holds 44 coins, all dimes and quarters, worth $8.60. How many of each are there?16 dimes, 28 quarters
A boat goes 92 miles downstream in 4 hours and 133 miles upstream in 7 hours. Find its speed in still water and the speed of the current.boat 21 mph, current 2 mph
Coffee at $1.50 a pound is mixed with coffee at $7.50 a pound to make 34 pounds of a blend worth $4.50 a pound. How many pounds of each?17 lb at $1.50, 17 lb at $7.50
Adult tickets cost $9 and child tickets $5. A total of 86 tickets were sold for $642. How many of each were sold?53 adult, 33 child
A boat goes 96 miles downstream in 4 hours and 48 miles upstream in 6 hours. Find its speed in still water and the speed of the current.boat 16 mph, current 8 mph
How many pounds of $1.50 coffee must be mixed with 2 pounds of $5.50 coffee to make a blend worth $3.10 a pound?3 lb
The sum of two numbers is 35 and their difference is 23. Find the two numbers.29 and 6
A boat goes 72 miles downstream in 3 hours and 40 miles upstream in 5 hours. Find its speed in still water and the speed of the current.boat 16 mph, current 8 mph
Using one equation for both facts. The count and the money are two separate statements, and mixing them into one equation leaves it unsolvable.
Also called systems of equations word problems, system word problems or two variable word problems.
What you can put on this worksheet
Systems of equations word problems
A jar holds 29 coins, all dimes and quarters, worth $5.30. How many of each are there?→ 13 dimes, 16 quarters
Current and wind
A boat goes 27 miles downstream in 1 hour and 39 miles upstream in 3 hours. Find its speed in still water and the speed of the current.→ boat 20 mph, current 7 mph
Mixtures
Coffee at $4.00 a pound is mixed with coffee at $7.00 a pound to make 28 pounds of a blend worth $5.50 a pound. How many pounds of each?→ 14 lb at $4.00, 14 lb at $7.00
Questions about these worksheets
Yes. Every systems of equations word problems sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the systems of equations word problems questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: systems of equations word problems, current and wind and mixtures. Tick as many as you want and set how many of each, or let it spread them evenly.
Using one equation for both facts. The count and the money are two separate statements, and mixing them into one equation leaves it unsolvable.