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 tables (x | y). Tents, x + y = 10: 4 | 6; 5 | 5; 6 | 4; 7 | 3. Campers, 2x + 4y = 28: 2 | 6; 4 | 5; 6 | 4; 8 | 3.

6. 3.

   Esme's camp has 10 tents: small ones for 2 campers (x) and big ones for 4 (y), 28 campers in all. Which pair (small tents, big tents) is in both tables?

   (6, 4)

7. 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.

8. 4.

   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)
9. 5.

   A lake camp has 12 sailboats: small ones with 1 seat (x) and big ones with 3 seats (y). Milo counts 22 seats. Which system fits?

   • x + 3y = 12 and x + y = 12
   • x + y = 12 and x + 3y = 22
   • x + y = 22 and x + 3y = 12
   • x + y = 12 and 3x + y = 22
10. 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
11. 7.

    Tala's team made 10 baskets, 2-pointers and 3-pointers, for 24 points. Could it be 6 two-pointers and 4 three-pointers?

    • No: it fits only the points.
    • No: it fits only the number of baskets.
    • No: it fits neither fact.
    • Yes: it fits both facts.
12. 8.

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

    • No: it fits neither fact.
    • No: it fits only the legs.
    • Yes: it fits both facts.
    • No: it fits only the number of animals.
13. 9.

    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 neither fact.
    • No: it fits only the campers.
    • No: it fits only the number of tents.
14. 10.

    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)