Word problems that need two equations
Grade 8 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
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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.
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?
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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.
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?
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 2x + 5y = 43
- x + y = 14 and 5x + 2y = 43
- x + y = 43 and 2x + 5y = 14
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 = 22 and x + 3y = 12
- x + y = 12 and x + 3y = 22
- x + y = 12 and 3x + y = 22
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 + 18 and y = -x + 30
- y = 4x + 30 and y = x + 18
- y = 30x - 4 and y = 18x - 1
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.
- Yes: it fits both facts.
- No: it fits neither fact.
- No: it fits only the number of baskets.
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.
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 number of tents.
- Yes: it fits both facts.
- No: it fits neither fact.
- No: it fits only the campers.
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)?
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).