Systems of equations word problems worksheet for Algebra 1
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.
Also taught in Algebra 2, at its own level and with its own examples.
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Pick more than one for a sheet that mixes them.
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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?
Adult tickets cost $13 and child tickets $9. A total of 58 tickets were sold for $654. How many of each were sold?
At a deli, 4 sandwiches and 1 drink cost $36, and 3 sandwiches and 5 drinks cost $44. Find the price of one sandwich and one drink.
A jar holds 56 coins, all dimes and quarters, worth $11.15. How many of each are there?
Adult tickets cost $16 and child tickets $5. A total of 96 tickets were sold for $1,415. How many of each were sold?
At a deli, 3 sandwiches and 4 drinks cost $43, and 2 sandwiches and 2 drinks cost $26. Find the price of one sandwich and one drink.
The sum of two numbers is 157 and their difference is 5. Find the two numbers.
Find speeds with wind or current
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.
A boat goes 92 miles downstream in 4 hours and 75 miles upstream in 5 hours. Find its speed in still water and the speed of the current.
A plane goes 495 miles with the wind in 1 hour and 1335 miles against the wind in 3 hours. Find its speed in still air and the speed of the wind.
A boat goes 25 miles downstream in 1 hour and 45 miles upstream in 3 hours. Find its speed in still water and the speed of the current.
A plane goes 305 miles with the wind in 1 hour and 860 miles against the wind in 4 hours. Find its speed in still air and the speed of the wind.
A boat goes 28 miles downstream in 2 hours and 60 miles upstream in 5 hours. Find its speed in still water and the speed of the current.
A plane goes 1200 miles with the wind in 3 hours and 1800 miles against the wind in 5 hours. Find its speed in still air and the speed of the wind.
Solve blend problems by price per pound
A shop wants 15 pounds of a mix to sell at $3.50 a pound. It mixes peanuts at $2.50 a pound with cashews at $5.00 a pound. How many pounds of each does it use?
A shop mixes 4 pounds of $3.50 grass seed with some $8.00 grass seed, and the mixture is worth $5.00 a pound. How many pounds of the $8.00 grass seed were used?
A shop has 4 pounds of $4.50 chocolates. How many pounds of $1.50 hard candy should it add to make a mix worth $2.30 a pound?
A 5-pound blend is worth $25.00 in all. It is made of coffee at $3.00 a pound and coffee at $8.00 a pound. How many pounds of each are in it?
A shop has 5 pounds of $6.00 tea. How many pounds of $2.00 tea should it add to make a blend worth $4.50 a pound?
A shop mixes 11 pounds of $2.50 peanuts with some $7.00 cashews, and the mix is worth $3.70 a pound. How many pounds of the $7.00 cashews were used?
Systems of Equations Word ProblemsAnswer keyVersion 1
Date Period
Use a system of equations to solve each problem.
Solve with a system of equations
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
Adult tickets cost $13 and child tickets $9. A total of 58 tickets were sold for $654. How many of each were sold?33 adult, 25 child
At a deli, 4 sandwiches and 1 drink cost $36, and 3 sandwiches and 5 drinks cost $44. Find the price of one sandwich and one drink.Sandwich $8,drink $4
A jar holds 56 coins, all dimes and quarters, worth $11.15. How many of each are there?19 dimes, 37 quarters
Adult tickets cost $16 and child tickets $5. A total of 96 tickets were sold for $1,415. How many of each were sold?85 adult, 11 child
At a deli, 3 sandwiches and 4 drinks cost $43, and 2 sandwiches and 2 drinks cost $26. Find the price of one sandwich and one drink.Sandwich $9,drink $4
The sum of two numbers is 157 and their difference is 5. Find the two numbers.81and 76
Find speeds with wind or current
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
A boat goes 92 miles downstream in 4 hours and 75 miles upstream in 5 hours. Find its speed in still water and the speed of the current.boat 19 mph, current 4 mph
A plane goes 495 miles with the wind in 1 hour and 1335 miles against the wind in 3 hours. Find its speed in still air and the speed of the wind.plane 470 mph, wind 25 mph
A boat goes 25 miles downstream in 1 hour and 45 miles upstream in 3 hours. Find its speed in still water and the speed of the current.boat 20 mph, current 5 mph
A plane goes 305 miles with the wind in 1 hour and 860 miles against the wind in 4 hours. Find its speed in still air and the speed of the wind.plane 260 mph, wind 45 mph
A boat goes 28 miles downstream in 2 hours and 60 miles upstream in 5 hours. Find its speed in still water and the speed of the current.boat 13 mph, current 1 mph
A plane goes 1200 miles with the wind in 3 hours and 1800 miles against the wind in 5 hours. Find its speed in still air and the speed of the wind.plane 380 mph, wind 20 mph
Solve blend problems by price per pound
A shop wants 15 pounds of a mix to sell at $3.50 a pound. It mixes peanuts at $2.50 a pound with cashews at $5.00 a pound. How many pounds of each does it use?9 lb at $2.50, 6 lb at $5.00
A shop mixes 4 pounds of $3.50 grass seed with some $8.00 grass seed, and the mixture is worth $5.00 a pound. How many pounds of the $8.00 grass seed were used?2 lb
A shop has 4 pounds of $4.50 chocolates. How many pounds of $1.50 hard candy should it add to make a mix worth $2.30 a pound?11 lb
A 5-pound blend is worth $25.00 in all. It is made of coffee at $3.00 a pound and coffee at $8.00 a pound. How many pounds of each are in it?3 lb at $3.00, 2 lb at $8.00
A shop has 5 pounds of $6.00 tea. How many pounds of $2.00 tea should it add to make a blend worth $4.50 a pound?3 lb
A shop mixes 11 pounds of $2.50 peanuts with some $7.00 cashews, and the mix is worth $3.70 a pound. How many pounds of the $7.00 cashews were used?4 lb
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 24 miles downstream in 1 hour and 48 miles upstream in 3 hours. Find its speed in still water and the speed of the current.→ boat 20 mph, current 4 mph
Mixtures
A shop has 18 pounds of $8.00 cashews. How many pounds of $3.50 peanuts should it add to make a mix worth $7.55 a pound?→ 2 lb
Large coefficients, wind and current
5 pounds of apples and 11 pounds of cherries cost $114. 8 pounds of apples and 12 pounds of cherries cost $132. Find the price per pound of each.→ Apples: $3, cherries: $9
Two-digit numbers and reversed digits
A two-digit number is 54 less than the number formed by reversing its digits, and its digits add up to 12. Find the number.→ 39
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 5: systems of equations word problems, current and wind, mixtures, large coefficients, wind and current and two-digit numbers and reversed digits. 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.