Skills · Linear Equations · Systems of Equations

Systems word problems

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

• a sum and a difference: Two numbers add to 20 and differ by 4.
• a count and a total at two prices: 20 tickets at $8 and $5 sell for $124.
• two totals, multiplied first: 3 muffins and 2 juices cost $13; 2 muffins and 5 juices cost $16.
• no solution (parallel lines): 3 muffins and 2 juices cost $13; 6 muffins and 4 juices cost $30.
• infinitely many solutions (same line): 3 muffins and 2 juices cost $13; 6 muffins and 4 juices cost $26.

Sample Sheet · Level 1

1. A quiz has 11 questions worth 19 points in all. Each question is worth 1 point or 2 points. Write (questions worth 1, questions worth 2).
2. A quiz has 10 questions worth 16 points in all. Each question is worth 1 point or 3 points. Write (questions worth 1, questions worth 3).
3. A quiz has 10 questions worth 18 points in all. Each question is worth 5 points or 1 point. Write (questions worth 5, questions worth 1).
4. A team played 25 games with no ties and lost 7 more games than it won. Write (wins, losses).
5. Two numbers add to 26 and differ by 8. Write (the smaller number, the larger number).
6. A team played 28 games with no ties and lost 6 more games than it won. Write (wins, losses).
7. A team played 15 games with no ties and lost 3 more games than it won. Write (wins, losses).
8. A quiz has 23 questions worth 56 points in all. Each question is worth 1 point or 4 points. Write (questions worth 1, questions worth 4).

Answer key

1. (3, 8)
2. (7, 3)
3. (2, 8)
4. (9, 16)
5. (9, 17)
6. (11, 17)
7. (6, 9)
8. (12, 11)

Sample Sheet · Level 3

1. A quiz has 35 questions worth 113 points in all. Each question is worth 4 points or 3 points. Write (questions worth 4, questions worth 3).
2. Two numbers add to 42 and differ by 10. Write (the smaller number, the larger number).
3. Two numbers add to 43 and differ by 5. Write (the smaller number, the larger number).
4. 2 adult and 3 student tickets cost $40. 6 adult and 9 student tickets cost $120. Write (the price of an adult ticket, the price of a student ticket).
5. 4 muffins and 6 juices cost $28. 2 muffins and 3 juices cost $11. Write (the price of a juice, the price of a muffin).
6. A play sold 33 tickets for $315. Adult tickets cost $11 and student tickets cost $7. Write (adult tickets, student tickets).
7. Renting 2 kayaks and 4 bikes for a day costs $108. Renting 5 kayaks and 3 bikes costs $186. Write (the daily price of a bike, the daily price of a kayak).
8. Renting 5 kayaks and 4 bikes for a day costs $160. Renting 4 kayaks and 5 bikes costs $155. Write (the daily price of a kayak, the daily price of a bike).

Answer key

1. (8, 27)
2. (16, 26)
3. (19, 24)
4. infinitely many solutions
5. no solution
6. (21, 12)
7. (12, 30)
8. (20, 15)

Make your own

Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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