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.

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

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

   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 + 2) − 14
   • 5n = 2(n + 1) + 14
   • 5n = 2(n + 2) + 14
3. 3.

   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 + 1)² = 85
   • n² + (n + 2)² = 85
   • (n + n + 1)² = 85
4. 4.

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

   9
5. 5.

   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
6. 6.

   Luz thinks of two consecutive positive odd integers. With n the smaller, the product is n(n + 2) = 99. What is n?

   9
7. 7.

   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
8. 8.

   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
9. 9.

   Cookies come in boxes of 12. Zee buys x boxes to get between 55 and 65 cookies, so 55 ≤ 12x ≤ 65. Which x makes sense?

   • x = 4.8
   • x = 4
   • x = 6
   • x = 5
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 = 6
    • x = −7