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

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Zee (and a very neat pencil) thinks of three consecutive even numbers that add to 78. The smallest is n. Which equation fits?

   • n + 2 + 4 = 78
   • n + n + n = 78
   • n + (n + 2) + (n + 4) = 78
   • n + (n + 1) + (n + 2) = 78
2. 2.

   Ari thinks of two consecutive integers with a product of 132. The smaller is n. Which equation fits?

   • n × n = 132
   • n(n + 2) = 132
   • n(n + 1) = 132
   • n + (n + 1) = 132
3. 3.

   Jun thinks of two consecutive positive integers. With n the smaller, the product is n(n + 1) = 90. What is n?

   9
4. 4.

   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?

   6
5. 5.

   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?

   8
6. 6.

   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?

   18
7. 7.

   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?

   16
8. 8.

   Tala's three consecutive even integers add to 42 less than 5 times the smallest. With n the smallest, that is 3n + 6 = 5n − 42. What is the largest?

   28
9. 9.

   A bus rental costs $40. Ari must spend between $150 and $170 on x buses, so 150 ≤ 40x ≤ 170. Which x makes sense?

   • x = 5
   • x = 4
   • x = −4
   • x = 3
10. 10.

    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 = 8
    • x = 7
    • x = −7
    • x = 6