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Grade 9 Systems of Equations Word Problems Worksheet with Answers

Grade 9 (US) · Year 10 (UK) · Class 9 (India) · Math

Unit 3: Systems of EquationsSolving SystemsCCSS A-CED.A.3

Setting up and solving two-variable systems from tickets, coins, mixtures and number puzzles. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Systems of Equations Word Problems

Grade 9 · Math

Score___ / 12

Name

Class

Date

Learning goal: Solving Systems · CCSS A-CED.A.3

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Two numbers add up to 24 and their difference is 10. What are the numbers?

Answer: 17 and 7

RememberSystems of equations

(3, 3)The solution is where the lines cross.Substitution: solve one equation for avariable, put it into the other.Elimination: add/subtract equationsso one variable cancels.
  1. 1

    A boat travels 27 km downstream in 3 hours and 3 km upstream in 3 hours. What is the speed of the boat in still water?

    Show your work
    Answer
  2. 2

    Apples cost $5 per bag and oranges cost $7 per bag. 32 bags cost $206. How many bags of apples were bought?

    Show your work
    Answer
  3. 3

    A theater sold 49 tickets. Adult tickets cost $11 and child tickets cost $2. Sales were $368. How many adult tickets were sold?

    Show your work
    Answer
  4. 4

    Two numbers add up to 49 and their difference is 7. What are the numbers?

    Show your work
    Answer
  5. 5

    Two numbers add up to 44 and their difference is 18. What are the numbers?

    Show your work
    Answer
  6. 6

    Apples cost $4 per bag and oranges cost $9 per bag. 51 bags cost $344. How many bags of apples were bought?

    Show your work
    Answer
  7. 7

    Two numbers add up to 58 and their difference is 10. What are the numbers?

    Show your work
    Answer
  8. 8

    A theater sold 53 tickets. Adult tickets cost $6 and child tickets cost $3. Sales were $264. How many adult tickets were sold?

    Show your work
    Answer
  9. 9

    Apples cost $3 per bag and oranges cost $9 per bag. 36 bags cost $156. How many bags of apples were bought?

    Show your work
    Answer
  10. 10

    A boat travels 27 km downstream in 3 hours and 9 km upstream in 3 hours. What is the speed of the boat in still water?

    Show your work
    Answer
  11. 11

    Apples cost $4 per bag and oranges cost $7 per bag. 56 bags cost $278. How many bags of apples were bought?

    Show your work
    Answer
  12. 12

    A theater sold 71 tickets. Adult tickets cost $13 and child tickets cost $10. Sales were $824. How many adult tickets were sold?

    Show your work
    Answer

★ Challenge corner for fast finishers

How many ways can a team of 2 be chosen from 5 students?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/9/systems_word

Answer key (click to show)
  1. 1.5 km/h
  2. 2.9
  3. 3.30
  4. 4.28 and 21
  5. 5.31 and 13
  6. 6.23
  7. 7.34 and 24
  8. 8.35
  9. 9.28
  10. 10.6 km/h
  11. 11.38
  12. 12.38
  13. ★10 (challenge corner)

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