Independent practice worksheet for solving consecutive integer problems.

Let's solve each problem from the "Consecutive Integer Problems - Independent Practice Worksheet" step by step.

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1. Find two consecutive even integers whose sum is 34.

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

$$
x + (x + 2) = 34 \\
2x + 2 = 34 \\
2x = 32 \\
x = 16
$$

So, the integers are:
16 and 18

✔ Answer: 16 and 18

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2. Find three consecutive integers whose sum is 72.

Let the integers be: $ x $, $ x+1 $, $ x+2 $

$$
x + (x+1) + (x+2) = 72 \\
3x + 3 = 72 \\
3x = 69 \\
x = 23
$$

So, the integers are:
23, 24, 25

✔ Answer: 23, 24, 25

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3. Three consecutive integers are such that three times the smallest is 12 more than the largest. Find the integers.

Let the integers be: $ x $, $ x+1 $, $ x+2 $

Three times the smallest: $ 3x $
Largest: $ x+2 $

Given:
$$
3x = (x+2) + 12 \\
3x = x + 14 \\
2x = 14 \\
x = 7
$$

So, the integers are:
7, 8, 9

✔ Answer: 7, 8, 9

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4. Find four consecutive integers whose sum is 82.

Let the integers be: $ x $, $ x+1 $, $ x+2 $, $ x+3 $

$$
x + (x+1) + (x+2) + (x+3) = 82 \\
4x + 6 = 82 \\
4x = 76 \\
x = 19
$$

So, the integers are:
19, 20, 21, 22

✔ Answer: 19, 20, 21, 22

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5. Find three consecutive even integers whose sum is 108.

Let the integers be: $ x $, $ x+2 $, $ x+4 $

$$
x + (x+2) + (x+4) = 108 \\
3x + 6 = 108 \\
3x = 102 \\
x = 34
$$

So, the integers are:
34, 36, 38

✔ Answer: 34, 36, 38

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6. Find five consecutive integers whose sum is 170.

Let the integers be: $ x $, $ x+1 $, $ x+2 $, $ x+3 $, $ x+4 $

$$
x + (x+1) + (x+2) + (x+3) + (x+4) = 170 \\
5x + 10 = 170 \\
5x = 160 \\
x = 32
$$

So, the integers are:
32, 33, 34, 35, 36

✔ Answer: 32, 33, 34, 35, 36

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7. Three consecutive integers are such that three times the smallest is 18 more than the largest. Find the integers.

Let the integers be: $ x $, $ x+1 $, $ x+2 $

Three times the smallest: $ 3x $
Largest: $ x+2 $

Given:
$$
3x = (x+2) + 18 \\
3x = x + 20 \\
2x = 20 \\
x = 10
$$

So, the integers are:
10, 11, 12

✔ Answer: 10, 11, 12

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8. Find two consecutive odd integers whose sum is 96.

Let the first odd integer be $ x $.
Next consecutive odd integer: $ x + 2 $

$$
x + (x+2) = 96 \\
2x + 2 = 96 \\
2x = 94 \\
x = 47
$$

So, the integers are:
47 and 49

✔ Answer: 47 and 49

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9. Three consecutive integers are such that three times the smallest is 22 more than the largest. Find the integers.

Let the integers be: $ x $, $ x+1 $, $ x+2 $

Three times smallest: $ 3x $
Largest: $ x+2 $

Given:
$$
3x = (x+2) + 22 \\
3x = x + 24 \\
2x = 24 \\
x = 12
$$

So, the integers are:
12, 13, 14

✔ Answer: 12, 13, 14

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10. Find three consecutive odd integers whose sum is 129.

Let the integers be: $ x $, $ x+2 $, $ x+4 $

$$
x + (x+2) + (x+4) = 129 \\
3x + 6 = 129 \\
3x = 123 \\
x = 41
$$

So, the integers are:
41, 43, 45

✔ Answer: 41, 43, 45

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✔ Final Answers Summary:

1. 16, 18
2. 23, 24, 25
3. 7, 8, 9
4. 19, 20, 21, 22
5. 34, 36, 38
6. 32, 33, 34, 35, 36
7. 10, 11, 12
8. 47, 49
9. 12, 13, 14
10. 41, 43, 45

Let me know if you'd like these explained in a different format or with visual steps!