Word problems that need two equations

Answer Key - Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Use this

   Two tables (x | y). Baskets, x + y = 12: 5 | 7; 6 | 6; 7 | 5; 8 | 4. Points, 2x + 3y = 29: 1 | 9; 4 | 7; 7 | 5; 10 | 3.

2. 1.

   Kira's team makes 12 baskets, some worth 2 points (x) and some 3 points (y), for 29 points. Which pair (2-pointers, 3-pointers) is in both tables?

   (7, 5)

3. Use this

   Two tables (x | y). Animals, x + y = 9: 3 | 6; 4 | 5; 5 | 4; 6 | 3. Legs, 2x + 4y = 26: 1 | 6; 3 | 5; 5 | 4; 7 | 3.

4. 2.

   At a farm, Ren counts 9 animals, ducks (x) and horses (y), with 26 legs in all. Which pair (ducks, horses) is in both tables?

   (5, 4)

5. Use this

   Two condition tables (x | y). Number of party tables, x + y = 7: 2 | 5; 3 | 4; 4 | 3; 5 | 2. Seats, 4x + 6y = 34: 1 | 5; 4 | 3; 7 | 1.

6. 3.

   Jun sets up 7 tables for a class party, some with 4 seats (x) and some with 6 (y), 34 seats in all. Which pair (4-seat, 6-seat) is in both condition tables?

   (4, 3)
7. 4.

   Luz's quiz has 14 questions: x are worth 2 points and y are worth 5 points. Luz could score 43 points in all. Which system fits?

   • 2x + 5y = 14 and 2x + 5y = 43
   • x + y = 14 and 5x + 2y = 43
   • x + y = 14 and 2x + 5y = 43
   • x + y = 43 and 2x + 5y = 14
8. 5.

   Noah's bean plant is 5 cm and grows 3 cm a week; the pea plant is 11 cm and grows 1 cm a week. Which system gives each height y after x weeks?

   • y = 3x + 11 and y = x + 5
   • y = 3x + 5 and y = x + 11
   • y = 8x and y = 12x
   • y = 5x + 3 and y = 11x + 1
9. 6.

   By Pia's fence, the sunny snowbank is 30 cm, losing 4 cm a day; the shady bank is 18 cm, losing 1 cm a day. Which system gives each depth y on day x?

   • y = -4x + 30 and y = -x + 18
   • y = 4x + 30 and y = x + 18
   • y = 30x - 4 and y = 18x - 1
   • y = -4x + 18 and y = -x + 30
10. 7.

    A field has 8 animals, ducks and horses, with 22 legs. Zee guesses 6 ducks and 2 horses. Does the guess fit the story?

    • Yes: it fits both facts.
    • No: it fits only the legs.
    • No: it fits neither fact.
    • No: it fits only the number of animals.
11. 8.

    A camp has 9 tents for 2 or 4 campers, with 26 campers in all. Ari guesses 7 small and 3 big tents. Does the guess fit the story?

    • Yes: it fits both facts.
    • No: it fits only the number of tents.
    • No: it fits only the campers.
    • No: it fits neither fact.
12. 9.

    Kira's roof: sunny snow is 36 cm, melting 5 cm a day; shady snow is 20 cm, melting 1 cm a day. The gap shrinks 4 cm a day. When are they equal (days, cm)?

    (4, 16)
13. 10.

    Luz: short book at page 10, +25 pages a day; long book at page 40, +10 a day. The gap shrinks 15 pages a day. When do the pages match? Give (days, page).

    (2, 60)