Matching worksheet for solving consecutive integer problems with word problems and corresponding answers.

To solve the problems, we will analyze each word problem step by step and match it with the correct answer from the provided options.

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Problem 1:

Three consecutive integers are such that three times the smallest is 26 more than the largest. Find the integers.

Let the three consecutive integers be \( x \), \( x+1 \), and \( x+2 \).

According to the problem:
\[ 3x = (x+2) + 26 \]

Simplify and solve for \( x \):
\[
3x = x + 2 + 26
\]
\[
3x = x + 28
\]
\[
3x - x = 28
\]
\[
2x = 28
\]
\[
x = 14
\]

So, the integers are:
\[ x = 14, \quad x+1 = 15, \quad x+2 = 16 \]

Answer: \( 14, 15, 16 \) (Option j)

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Problem 2:

Find two consecutive odd integers whose sum is 88.

Let the two consecutive odd integers be \( x \) and \( x+2 \).

According to the problem:
\[ x + (x+2) = 88 \]

Simplify and solve for \( x \):
\[
x + x + 2 = 88
\]
\[
2x + 2 = 88
\]
\[
2x = 86
\]
\[
x = 43
\]

So, the integers are:
\[ x = 43, \quad x+2 = 45 \]

Answer: \( 43, 45 \) (Option g)

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Problem 3:

Find three consecutive integers whose sum is 96.

Let the three consecutive integers be \( x \), \( x+1 \), and \( x+2 \).

According to the problem:
\[ x + (x+1) + (x+2) = 96 \]

Simplify and solve for \( x \):
\[
x + x + 1 + x + 2 = 96
\]
\[
3x + 3 = 96
\]
\[
3x = 93
\]
\[
x = 31
\]

So, the integers are:
\[ x = 31, \quad x+1 = 32, \quad x+2 = 33 \]

Answer: \( 31, 32, 33 \) (Option i)

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Problem 4:

Find four consecutive integers whose sum is 110.

Let the four consecutive integers be \( x \), \( x+1 \), \( x+2 \), and \( x+3 \).

According to the problem:
\[ x + (x+1) + (x+2) + (x+3) = 110 \]

Simplify and solve for \( x \):
\[
x + x + 1 + x + 2 + x + 3 = 110
\]
\[
4x + 6 = 110
\]
\[
4x = 104
\]
\[
x = 26
\]

So, the integers are:
\[ x = 26, \quad x+1 = 27, \quad x+2 = 28, \quad x+3 = 29 \]

Answer: \( 26, 27, 28, 29 \) (Option h)

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Problem 5:

Three consecutive integers are such that three times the smallest is 32 more than the largest. Find the integers.

Let the three consecutive integers be \( x \), \( x+1 \), and \( x+2 \).

According to the problem:
\[ 3x = (x+2) + 32 \]

Simplify and solve for \( x \):
\[
3x = x + 2 + 32
\]
\[
3x = x + 34
\]
\[
3x - x = 34
\]
\[
2x = 34
\]
\[
x = 17
\]

So, the integers are:
\[ x = 17, \quad x+1 = 18, \quad x+2 = 19 \]

Answer: \( 17, 18, 19 \) (Option f)

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Problem 6:

Find two consecutive even integers whose sum is 45.

Let the two consecutive even integers be \( x \) and \( x+2 \).

According to the problem:
\[ x + (x+2) = 45 \]

Simplify and solve for \( x \):
\[
x + x + 2 = 45
\]
\[
2x + 2 = 45
\]
\[
2x = 43
\]

Since 43 is not divisible by 2, there are no two consecutive even integers whose sum is 45. This problem has no solution in the given options.

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Problem 7:

Find four consecutive integers whose sum is 62.

Let the four consecutive integers be \( x \), \( x+1 \), \( x+2 \), and \( x+3 \).

According to the problem:
\[ x + (x+1) + (x+2) + (x+3) = 62 \]

Simplify and solve for \( x \):
\[
x + x + 1 + x + 2 + x + 3 = 62
\]
\[
4x + 6 = 62
\]
\[
4x = 56
\]
\[
x = 14
\]

So, the integers are:
\[ x = 14, \quad x+1 = 15, \quad x+2 = 16, \quad x+3 = 17 \]

Answer: \( 14, 15, 16, 17 \) (Option d)

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Problem 8:

Find four consecutive even integers whose sum is 100.

Let the four consecutive even integers be \( x \), \( x+2 \), \( x+4 \), and \( x+6 \).

According to the problem:
\[ x + (x+2) + (x+4) + (x+6) = 100 \]

Simplify and solve for \( x \):
\[
x + x + 2 + x + 4 + x + 6 = 100
\]
\[
4x + 12 = 100
\]
\[
4x = 88
\]
\[
x = 22
\]

So, the integers are:
\[ x = 22, \quad x+2 = 24, \quad x+4 = 26, \quad x+6 = 28 \]

Answer: \( 22, 24, 26, 28 \) (Option c)

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Problem 9:

Find three consecutive odd integers whose sum is 135.

Let the three consecutive odd integers be \( x \), \( x+2 \), and \( x+4 \).

According to the problem:
\[ x + (x+2) + (x+4) = 135 \]

Simplify and solve for \( x \):
\[
x + x + 2 + x + 4 = 135
\]
\[
3x + 6 = 135
\]
\[
3x = 129
\]
\[
x = 43
\]

So, the integers are:
\[ x = 43, \quad x+2 = 45, \quad x+4 = 47 \]

Answer: \( 43, 45, 47 \) (Option b)

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Problem 10:

Find two consecutive integers whose sum is 55.

Let the two consecutive integers be \( x \) and \( x+1 \).

According to the problem:
\[ x + (x+1) = 55 \]

Simplify and solve for \( x \):
\[
x + x + 1 = 55
\]
\[
2x + 1 = 55
\]
\[
2x = 54
\]
\[
x = 27
\]

So, the integers are:
\[ x = 27, \quad x+1 = 28 \]

Answer: \( 27, 28 \) (Option a)

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Final Answers:

1. \( \boxed{j} \)
2. \( \boxed{g} \)
3. \( \boxed{i} \)
4. \( \boxed{h} \)
5. \( \boxed{f} \)
6. No solution
7. \( \boxed{d} \)
8. \( \boxed{c} \)
9. \( \boxed{b} \)
10. \( \boxed{a} \)

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Summary of Matches:

- 1 → j
- 2 → g
- 3 → i
- 4 → h
- 5 → f
- 6 → No solution
- 7 → d
- 8 → c
- 9 → b
- 10 → a

Final Answer Boxed:
\[
\boxed{j, g, i, h, f, \text{No solution}, d, c, b, a}
\]