Integer Word Problems worksheet with 11 questions requiring students to find integers based on given sums and conditions.

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 one 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 integers are:
$$
x = 30 \quad \text{and} \quad x + 1 = 31
$$

✔ Answer: The two consecutive 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 three consecutive integers be:
$$ x, \quad x+1, \quad x+2 $$

Their sum is:
$$
x + (x+1) + (x+2) = 51
$$

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

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

Divide by 3:
$$
x = 16
$$

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

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

✔ Answer: The largest integer is 18.

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✔ Summary of Answers:

- Question 1: The two consecutive integers are 30 and 31.
- Question 3: The largest of the three consecutive integers is 18.

> 💡 Tip: Always define your variable clearly (e.g., let $ x $ be the first number), then express others in terms of $ x $. Then write an equation based on the total sum or other condition.

Would you like me to solve more problems from this sheet? For example, odd/even consecutive integers or word problems involving expressions like “four times the next” — those are great for practice!