Number puzzles (consecutive numbers), and checking that an answer fits the story
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?
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?
Pia says two consecutive integers can have squares that add to 61. Can this happen?
- Yes: n = 5, since 5² + 6² = 25 + 36 = 61
- No: 61 is not a perfect square, so it cannot be a sum of squares
- No: a sum of two squares must be even
- Yes: n = 5.5, halfway between the sides
Ren says two consecutive even integers can have a product of 150. Can this happen?
- No: 10 × 12 = 120 and 12 × 14 = 168, so 150 is skipped
- Yes: n ≈ 11.3, so the numbers are 11.3 and 13.3
- Yes: any total works for even numbers
- Yes: n = 12 gives 12 × 14 = 168, which is close enough to 150
Tala says two consecutive odd integers can have a product of 195. Can this happen?
- Yes: n = 14, the middle of 13 and 15
- No: a product of consecutive numbers must be even
- Yes: n = 13, since 13 × 15 = 195
- No: 195 cannot be split into two equal numbers
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?
Bo has $11 and saves $4 each week for a $50 gift. What is the fewest whole weeks until Bo has enough?
A trip has 135 students and 27 adults. Each bus holds 40 people. What is the fewest whole buses Esme must book?