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.

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

   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
3. 3.

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

   9
4. 4.

   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
5. 5.

   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?

   21
6. 6.

   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
7. 7.

   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 = 5
   • x = 4
   • x = 6
   • x = 4.8
8. 8.

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

   • x = 3
   • x = 4
   • x = −4
   • x = 5
9. 9.

   Bo reads x whole pages a day for 7 days and wants more than 100 but fewer than 112 pages, so 100 < 7x < 112. Which x makes sense?

   • x = 15
   • x = 15.5
   • x = 14
   • x = 16
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 = 7
    • x = 6
    • x = 8
    • x = −7