Number puzzles (consecutive numbers), and checking that an answer fits the story
Grade 9 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Zee (and a very neat pencil) thinks of three consecutive even numbers that add to 78. The smallest is n. Which equation fits?
- n + (n + 1) + (n + 2) = 78
- n + n + n = 78
- n + 2 + 4 = 78
- n + (n + 2) + (n + 4) = 78
Ari thinks of two consecutive integers with a product of 132. The smaller is n. Which equation fits?
- n + (n + 1) = 132
- n(n + 1) = 132
- n × n = 132
- n(n + 2) = 132
Bo thinks of two consecutive even numbers. Five times the smaller is 14 more than twice the larger. The smaller is n. Which equation fits?
- 5n = 2n + 14
- 5n = 2(n + 1) + 14
- 5n = 2(n + 2) + 14
- 5n = 2(n + 2) − 14
Esme thinks of two consecutive integers. The sum of their squares is 85. The smaller is n. Which equation fits?
- n² + n² = 85
- n² + (n + 2)² = 85
- n² + (n + 1)² = 85
- (n + n + 1)² = 85
Kira thinks of two consecutive positive integers whose squares add to 85. With n the smaller, that is n² + (n + 1)² = 85. What is n?
Milo thinks of two consecutive positive integers. The square of the smaller is 55 more than the larger, so n² = (n + 1) + 55. What is n?
Noah's three consecutive integers add to 13 less than 4 times the smallest. With n the smallest, that is 3n + 3 = 4n − 13. What is the largest?
Pia's four consecutive integers add to 30 less than 6 times the smallest. With n the smallest, that is 4n + 6 = 6n − 30. What is the largest?
Ren's five consecutive integers add to 34 more than 3 times the smallest. With n the smallest, that is 5n + 10 = 3n + 34. What is the largest?
A team has 13 players and adds x players. The team needs more than 19 but fewer than 21 players, so 19 < 13 + x < 21. Esme asks which x makes sense.
- x = 7
- x = 6
- x = −7
- x = 8