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. 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?

   • x + y = 14 and 2x + 5y = 43
   • x + y = 43 and 2x + 5y = 14
   • 2x + 5y = 14 and 2x + 5y = 43
   • x + y = 14 and 5x + 2y = 43
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 = 5x + 3 and y = 11x + 1
   • y = 8x and y = 12x
   • y = 3x + 5 and y = x + 11
   • y = 3x + 11 and y = x + 5
9. 6.

   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 number of baskets.
   • Yes: it fits both facts.
   • No: it fits only the points.
   • No: it fits neither fact.
10. 7.

    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?

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

    Bo's bean plant is 6 cm, growing 3 cm a week; the pea plant is 18 cm, growing 1 cm a week. The gap shrinks 2 cm a week. When are they equal (weeks, cm)?

    (6, 24)
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)