Worksheet titled "Integer Word Problems" featuring 11 math problems involving consecutive integers, odd and even integers, and algebraic expressions. Students are instructed to complete at least two questions from each section and show their work.

Let's solve two questions from Section 1 of the "Integer Word Problems" worksheet. I'll choose Question 1 and Question 3, as they are good examples of consecutive integer problems and will help build foundational skills.

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✔ Question 1:

The sum of two consecutive integers is 61. Find the two integers.

#### Step-by-step Solution:

Let the first integer be:
$$ x $$

Since the integers are consecutive, the next integer is:
$$ x + 1 $$

Their sum is given as 61:
$$
x + (x + 1) = 61
$$

Simplify:
$$
2x + 1 = 61
$$

Subtract 1 from both sides:
$$
2x = 60
$$

Divide by 2:
$$
x = 30
$$

So, the two consecutive integers are:
$$
x = 30 \quad \text{and} \quad x + 1 = 31
$$

✔ Answer: The two integers are 30 and 31.

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✔ Question 3:

The sum of three consecutive integers is 51. Find the largest integer.

#### Step-by-step Solution:

Let the first integer be:
$$ x $$

Then the next two consecutive integers are:
$$ x + 1 \quad \text{and} \quad x + 2 $$

Sum of the three integers:
$$
x + (x + 1) + (x + 2) = 51
$$

Simplify:
$$
3x + 3 = 51
$$

Subtract 3 from both sides:
$$
3x = 48
$$

Divide by 3:
$$
x = 16
$$

So the three integers are:
$$
16, \; 17, \; 18
$$

The largest integer is:
$$
\boxed{18}
$$

✔ Answer: The largest integer is 18.

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📝 Summary of Solutions:

- Q1: The two consecutive integers are 30 and 31.
- Q3: The largest of the three consecutive integers is 18.

These solutions demonstrate how to model word problems using algebraic expressions and solve for unknowns step by step.

Would you like me to solve more questions (e.g., odd/even consecutive integers or more complex ones)?