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Equations and inequalities · Ages 13–14

From words to simultaneous equations worksheet

Part of: Simultaneous linear equations

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From words to simultaneous equations worksheet

Equations and inequalities · Ages 13–14

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

Part A: Working out and filling in (2 marks each)

  1. 1.Two numbers add to 79 and differ by 11. With x the larger and y the smaller: x + y = , x − y = , so x = .

    Fill in each blank

    Answer:

  2. 2.Chickens and rabbits: x + y = 14, 2x + 4y = 38 (x chickens, y rabbits). Double the first and take it from the second: y =

    Answer:

Part B: Choose, or true or false (2 marks each)

  1. 3.A pen holds chickens and rabbits, 25 heads and 72 legs. With x chickens and y rabbits, which pair of equations is right?

    • A. x + y = 72, 2x + 4y = 25
    • B. x + y = 25, 2x + 4y = 72
    • C. x + y = 25, 4x + 2y = 72
    • D. x + y = 25, 2x + 2y = 72

    Choose the right answer

    Answer:

  2. 4.An adult ticket is $x and a child's $y. 1 adult and 3 child tickets cost $330; 1 adult and 2 child tickets cost $260. Which pair of equations is right?

    • A. x + 3y = 330, x + 2y = 260
    • B. x + 3y = 260, x + 2y = 330
    • C. x + 3y = 330, 2x + y = 260
    • D. 3x + y = 330, 2x + y = 260

    Choose the right answer

    Answer:

  3. 5.A two-digit number has tens digit x and ones digit y. Its digits add to 13; swapping them makes a number 9 larger. Which pair of equations is right?

    • A. x + y = 13, (10x + y) − (10y + x) = 9
    • B. x + y = 13, 10y − 10x = 9
    • C. x + y = 13, (10y + x) − (10x + y) = 9
    • D. 10x + y = 13, (10y + x) − (10x + y) = 9

    Choose the right answer

    Answer:

  4. 6.An apple is $x and an orange $y. 4 apples and 5 oranges cost $115, and an apple costs $4 more than an orange. Which pair of equations is right?

    • A. 4x + 5y = 115, x + y = 4
    • B. 5x + 4y = 115, x − y = 4
    • C. 4x + 5y = 115, x − y = 4
    • D. 4x + 5y = 115, y − x = 4

    Choose the right answer

    Answer:

  5. 7.A has $6 more than B, and they have $50 together. With A's money $x and B's $y, this is x + y = 50 and x − y = 6.

    True or false?

    Answer:

  6. 8.An apple is $x and an orange $y. 5 apples and 2 oranges cost $26, and an apple costs $1 more than an orange. Which pair of equations is right?

    • A. 5x + 2y = 26, y − x = 1
    • B. 5x + 2y = 26, x − y = 1
    • C. 5x + 2y = 26, x + y = 1
    • D. 2x + 5y = 26, x − y = 1

    Choose the right answer

    Answer:

  7. 9.A has $14 more than B, and they have $76 together. With A's money $x and B's $y, this is x + y = 76 and x − y = 14.

    True or false?

    Answer:

  8. 10.A rectangle's perimeter is 38 cm, and its length is 5 cm less than 3 times its width. With length x cm and width y cm, which pair of equations is right?

    • A. 2x + 2y = 38, x = 3y − 5
    • B. x + y = 38, x = 3y − 5
    • C. 2x + 2y = 38, y = 3x − 5
    • D. 2x + 2y = 38, x = 3(y − 5)

    Choose the right answer

    Answer:

  9. 11.If Ka-lok gives Tsz-hin $8, they have the same; if Tsz-hin gives Ka-lok $8, Ka-lok has 5 times as much as Tsz-hin. With $x as Ka-lok's and $y as Tsz-hin's, which pair of equations is right?

    • A. x − 8 = y, x + 8 = 5(y − 8)
    • B. x − 8 = y + 8, 5(x + 8) = y − 8
    • C. x − 8 = y + 8, x + 8 = 5y − 8
    • D. x − 8 = y + 8, x + 8 = 5(y − 8)

    Choose the right answer

    Answer:

  10. 12.A rectangle's perimeter is 58 cm, and its length is 3 cm less than 3 times its width. With length x cm and width y cm, which pair of equations is right?

    • A. 2x + 2y = 58, x = 3y − 3
    • B. x + y = 58, x = 3y − 3
    • C. 2x + 2y = 58, x = 3(y − 3)
    • D. 2x + 2y = 58, y = 3x − 3

    Choose the right answer

    Answer:

Part C: Word problems (4 marks each)

  1. 13.x g of 10% salt water is mixed with y g of 30% salt water, giving 200 g at 15%. Which pair of equations is right?

    • A. x + y = 200, 10x + 30y = 3000
    • B. x + y = 200, 10x + 30y = 15
    • C. x + y = 200, 30x + 10y = 3000
    • D. 10x + 30y = 200, x + y = 3000

    Choose the right answer

    Working:

    Answer:

  2. 14.4 years ago, A was 3 times as old as B; now their ages add to 28. With A x and B y years old now, which pair of equations is right?

    • A. x + y = 28, x − 4 = 3y − 4
    • B. x + y = 28 − 4, x − 4 = 3(y − 4)
    • C. x + y = 28, x + 4 = 3(y + 4)
    • D. x + y = 28, x − 4 = 3(y − 4)

    Choose the right answer

    Working:

    Answer:

  3. 15.Concert tickets: zone A $220 each, zone B $100 each; 101 sold for $13,460. With x zone A tickets and y zone B, which pair of equations is right?

    • A. x + y = 101, 100x + 220y = 13460
    • B. x + y = 13460, 220x + 100y = 101
    • C. x + y = 101, 220x − 100y = 13460
    • D. x + y = 101, 220x + 100y = 13460

    Choose the right answer

    Working:

    Answer:

  4. 16."3 times x is 17 less than y" can be written y − 3x = −17.

    True or false?

    Working:

    Answer:

  5. 17.A two-digit number has tens digit x and ones digit y. Its digits add to 9, and the number is 5 times its digit sum. Which pair of equations is right?

    • A. x + y = 9, 10x + y = 5(x + y)
    • B. x + y = 9, xy = 5(x + y)
    • C. x + y = 9, 10y + x = 5(x + y)
    • D. x + y = 9, 10x + y = 5x + y

    Choose the right answer

    Working:

    Answer:

  6. 18.Concert tickets: zone A $280 each, zone B $100 each; 60 sold for $11,760. How many zone A tickets were sold?

    Working:

    Answer:

Show the answers and working

From words to simultaneous equations worksheet: Answers and working

Part A: Working out and filling in

  1. 1. 79, 11, 45

    Sum: x + y = 79; difference: x − y = 11. Adding, 2x = 79 + 11, x = 45.

  2. 2. 5

    2x + 2y = 28; (2x + 4y) − (2x + 2y) = 38 − 28, so 2y = 10 and y = 5.

Part B: Choose, or true or false

  1. 3. B. x + y = 25, 2x + 4y = 72

    Heads: x + y = 25. Legs: 2 a chicken and 4 a rabbit, 2x + 4y = 72.

  2. 4. A. x + 3y = 330, x + 2y = 260

    Total = number × price, one equation per order: x + 3y = 330, x + 2y = 260.

  3. 5. C. x + y = 13, (10y + x) − (10x + y) = 9

    The number is 10x + y and the swapped one 10y + x. Digits: x + y = 13; swapped minus original = 9.

  4. 6. C. 4x + 5y = 115, x − y = 4

    Total: 4x + 5y = 115; difference: x − y = 4.

  5. 7. True

    A has more, so x − y is the positive 6.

  6. 8. B. 5x + 2y = 26, x − y = 1

    Total: 5x + 2y = 26; difference: x − y = 1.

  7. 9. True

    A has more, so x − y is the positive 14.

  8. 10. A. 2x + 2y = 38, x = 3y − 5

    Perimeter: 2x + 2y = 38; length from width: x = 3y − 5. Try x = 13, y = 6: both hold.

  9. 11. D. x − 8 = y + 8, x + 8 = 5(y − 8)

    Each time, the giver has $8 less and the receiver $8 more. First: x − 8 = y + 8; second: x + 8 = 5(y − 8). Try x = 32, y = 16: both hold.

  10. 12. A. 2x + 2y = 58, x = 3y − 3

    Perimeter: 2x + 2y = 58; length from width: x = 3y − 3. Try x = 21, y = 8: both hold.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

  1. 13. A. x + y = 200, 10x + 30y = 3000

    Weight: x + y = 200; salt (times 100): 10x + 30y = 15 × 200 = 3000.

  2. 14. D. x + y = 28, x − 4 = 3(y − 4)

    Now: x + y = 28; 4 years ago, A was x − 4 and B y − 4: x − 4 = 3(y − 4).

  3. 15. D. x + y = 101, 220x + 100y = 13460

    Tickets: x + y = 101; takings: 220x + 100y = 13460.

  4. 16. False

    3x is 17 less than y, so y is 17 more than 3x: y − 3x = 17.

  5. 17. A. x + y = 9, 10x + y = 5(x + y)

    Digits: x + y = 9; the number 10x + y is 5 times the digit sum: 10x + y = 5(x + y).

  6. 18. 32 tickets

    x + y = 60, 280x + 100y = 11760. Take 100 times the first from the second: (280 − 100)x = 11760 − 100 × 60, x = 32.

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