Number Problems worksheet with ten word problems about finding consecutive even and odd numbers based on their sums.

Let’s solve each problem one by one. We’ll use simple steps and check our work as we go.

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Problem 1: The sum of two consecutive even numbers is 34. What are the numbers?

Consecutive even numbers differ by 2 (like 2 and 4, or 10 and 12).

Let the first even number be x.
Then the next consecutive even number is x + 2.

Their sum:
x + (x + 2) = 34
→ 2x + 2 = 34
→ 2x = 32
→ x = 16

So the numbers are 16 and 18.

Check: 16 + 18 = 34 ✔

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Problem 2: The sum of four consecutive odd numbers is 24. Find the numbers.

Consecutive odd numbers differ by 2 (like 1, 3, 5, 7).

Let the first odd number be x.
Then the next three are: x+2, x+4, x+6

Sum:
x + (x+2) + (x+4) + (x+6) = 24
→ 4x + 12 = 24
→ 4x = 12
→ x = 3

Numbers: 3, 5, 7, 9

Check: 3+5=8, 7+9=16 → 8+16=24 ✔

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Problem 3: The sum of two consecutive even numbers is 26. What are the numbers?

Same method as Problem 1.

x + (x+2) = 26
→ 2x + 2 = 26
→ 2x = 24
→ x = 12

Numbers: 12 and 14

Check: 12 + 14 = 26 ✔

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Problem 4: The sum of four consecutive odd numbers is 64. Find the numbers.

x + (x+2) + (x+4) + (x+6) = 64
→ 4x + 12 = 64
→ 4x = 52
→ x = 13

Numbers: 13, 15, 17, 19

Check: 13+15=28, 17+19=36 → 28+36=64 ✔

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Problem 5: The sum of three consecutive odd numbers is 63. Find the numbers.

Let them be: x, x+2, x+4

Sum: x + (x+2) + (x+4) = 63
→ 3x + 6 = 63
→ 3x = 57
→ x = 19

Numbers: 19, 21, 23

Check: 19+21=40, 40+23=63 ✔

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Problem 6: The sum of three consecutive even numbers is 12. What are the numbers?

x + (x+2) + (x+4) = 12
→ 3x + 6 = 12
→ 3x = 6
→ x = 2

Numbers: 2, 4, 6

Check: 2+4+6=12 ✔

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Problem 7: The sum of three consecutive even numbers is 48. What are the numbers?

x + (x+2) + (x+4) = 48
→ 3x + 6 = 48
→ 3x = 42
→ x = 14

Numbers: 14, 16, 18

Check: 14+16=30, 30+18=48 ✔

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Problem 8: The sum of four consecutive odd numbers is 80. Find the numbers.

x + (x+2) + (x+4) + (x+6) = 80
→ 4x + 12 = 80
→ 4x = 68
→ x = 17

Numbers: 17, 19, 21, 23

Check: 17+19=36, 21+23=44 → 36+44=80 ✔

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Problem 9: The sum of two consecutive even numbers is 22. What are the numbers?

x + (x+2) = 22
→ 2x + 2 = 22
→ 2x = 20
→ x = 10

Numbers: 10 and 12

Check: 10+12=22 ✔

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Problem 10: The sum of two consecutive odd numbers is 24. Find the numbers.

Odd numbers also differ by 2.

x + (x+2) = 24
→ 2x + 2 = 24
→ 2x = 22
→ x = 11

Numbers: 11 and 13

Check: 11+13=24 ✔

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Final Answer:

1. 16 and 18
2. 3, 5, 7, 9
3. 12 and 14
4. 13, 15, 17, 19
5. 19, 21, 23
6. 2, 4, 6
7. 14, 16, 18
8. 17, 19, 21, 23
9. 10 and 12
10. 11 and 13