Number puzzles (consecutive numbers), and checking that an answer fits the story

Grade 9 Math Worksheet - Challenge Me

NameDate

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

Jun picks three consecutive positive integers. The product of the two smaller is 12 more than 6 times the largest. What is the smallest?
Kira picks three consecutive even integers. The square of the largest is 52 more than the product of the other two. What is the smallest?
Luz picks three consecutive positive odd integers. The squares of the smallest and the largest add to 152 more than twice the middle one. What is the smallest?
Milo picks three consecutive even integers, which may be negative. Five times the largest minus 3 times the smallest is 20 more than 4 times the middle. What is the smallest?
5.
Noah says two consecutive integers can have a product of 100. Can this happen?
- Yes: n = 10 gives 10 × 11 = 110, which is close enough to 100
- No: 9 × 10 = 90 and 10 × 11 = 110, so 100 is skipped
- Yes: n ≈ 9.5, so the numbers are 9.5 and 10.5
- Yes: any total works for consecutive products
6.
Pia says two consecutive integers can have squares that add to 61. Can this happen?
- No: a sum of two squares must be even
- Yes: n = 5.5, halfway between the sides
- No: 61 is not a perfect square, so it cannot be a sum of squares
- Yes: n = 5, since 5² + 6² = 25 + 36 = 61
7.
Ren says two consecutive even integers can have a product of 150. Can this happen?
- Yes: n = 12 gives 12 × 14 = 168, which is close enough to 150
- No: 10 × 12 = 120 and 12 × 14 = 168, so 150 is skipped
- Yes: any total works for even numbers
- Yes: n ≈ 11.3, so the numbers are 11.3 and 13.3
8.
Tala says two consecutive odd integers can have a product of 195. Can this happen?
- No: 195 cannot be split into two equal numbers
- Yes: n = 14, the middle of 13 and 15
- Yes: n = 13, since 13 × 15 = 195
- No: a product of consecutive numbers must be even
A lift holds 450 kg. A cart weighs 35 kg and each box weighs 60 kg. At most how many whole boxes can Ari load on the cart?
A trip has 135 students and 27 adults. Each bus holds 40 people. What is the fewest whole buses Esme must book?

Number puzzles (consecutive numbers), and checking that an answer fits the story

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

Jun picks three consecutive positive integers. The product of the two smaller is 12 more than 6 times the largest. What is the smallest?
8
Kira picks three consecutive even integers. The square of the largest is 52 more than the product of the other two. What is the smallest?
6
Luz picks three consecutive positive odd integers. The squares of the smallest and the largest add to 152 more than twice the middle one. What is the smallest?
7
Milo picks three consecutive even integers, which may be negative. Five times the largest minus 3 times the smallest is 20 more than 4 times the middle. What is the smallest?
-4
5.
Noah says two consecutive integers can have a product of 100. Can this happen?
- Yes: n = 10 gives 10 × 11 = 110, which is close enough to 100
- No: 9 × 10 = 90 and 10 × 11 = 110, so 100 is skipped
- Yes: n ≈ 9.5, so the numbers are 9.5 and 10.5
- Yes: any total works for consecutive products
6.
Pia says two consecutive integers can have squares that add to 61. Can this happen?
- No: a sum of two squares must be even
- Yes: n = 5.5, halfway between the sides
- No: 61 is not a perfect square, so it cannot be a sum of squares
- Yes: n = 5, since 5² + 6² = 25 + 36 = 61
7.
Ren says two consecutive even integers can have a product of 150. Can this happen?
- Yes: n = 12 gives 12 × 14 = 168, which is close enough to 150
- No: 10 × 12 = 120 and 12 × 14 = 168, so 150 is skipped
- Yes: any total works for even numbers
- Yes: n ≈ 11.3, so the numbers are 11.3 and 13.3
8.
Tala says two consecutive odd integers can have a product of 195. Can this happen?
- No: 195 cannot be split into two equal numbers
- Yes: n = 14, the middle of 13 and 15
- Yes: n = 13, since 13 × 15 = 195
- No: a product of consecutive numbers must be even
A lift holds 450 kg. A cart weighs 35 kg and each box weighs 60 kg. At most how many whole boxes can Ari load on the cart?
6
A trip has 135 students and 27 adults. Each bus holds 40 people. What is the fewest whole buses Esme must book?
5