Integer Word Problems Worksheets - Math Monks - Free Printable

Let's solve each of the integer word problems step by step and explain the reasoning.

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1. Benny has $75 to spend. He purchased a gift for $93. If he borrows the extra money that he needs, how much does he need to borrow?

- Benny has $75, but the gift costs $93.
- The difference is:
$ 93 - 75 = 18 $
- So, he needs to borrow $18.

✔ Answer: $18

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2. The top of a mountain is 1270 feet above sea level. The bottom of a valley is 650 feet below sea level. How high is the mountain top from the bottom of the valley?

- Mountain top: +1270 ft (above sea level)
- Valley bottom: –650 ft (below sea level)
- To find the total vertical distance between them:
$ 1270 - (-650) = 1270 + 650 = 1920 $ feet

✔ Answer: 1920 feet

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3. A football team scores 3 goals in the first half and 2 in the second half. However, the opponent team scored 3 goals in the whole game. Which team has won, and by how many goals?

- Our team: $ 3 + 2 = 5 $ goals
- Opponent team: $ 3 $ goals
- Difference: $ 5 - 3 = 2 $

Our team wins by 2 goals.

✔ Answer: Our team won by 2 goals

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4. Twice a number added to half of itself equals 24. Find the number.

Let the number be $ x $.

According to the problem:
$$
2x + \frac{1}{2}x = 24
$$

Combine like terms:
$$
\left(2 + \frac{1}{2}\right)x = \frac{5}{2}x = 24
$$

Now solve for $ x $:
$$
x = 24 \div \frac{5}{2} = 24 \times \frac{2}{5} = \frac{48}{5} = 9.6
$$

Wait! But the problem says "twice a number added to half of itself" — this is an algebraic equation, and we can check:

Let’s test $ x = 9.6 $:
- Twice: $ 2 \times 9.6 = 19.2 $
- Half: $ 0.5 \times 9.6 = 4.8 $
- Sum: $ 19.2 + 4.8 = 24 $ ✔

So, the number is 9.6, or as a fraction: $ \frac{48}{5} $

But since the worksheet is about integers, let's double-check if there was a misinterpretation.

Wait — maybe it's asking for an integer solution?

But $ 9.6 $ is not an integer.

Let’s recheck the math:

$$
2x + \frac{1}{2}x = 24 \\
\Rightarrow \frac{5}{2}x = 24 \\
\Rightarrow x = 24 \times \frac{2}{5} = \frac{48}{5} = 9.6
$$

No integer satisfies this exactly. But perhaps the problem expects the answer as a decimal or fraction.

Since the problem doesn’t specify that the number must be an integer, we go with the exact value.

✔ Answer: 9.6 or $ \frac{48}{5} $

But wait — maybe the problem meant "twice a number plus half of another number"? No, it says "half of itself".

So unless there's a typo, the answer is 9.6.

However, let’s consider if the problem meant something else — perhaps “twice a number added to half of itself” — which is correct.

Alternatively, could it be a typo and they meant “a number plus half of itself”? That would give $ 1.5x = 24 $ → $ x = 16 $. But no, it says twice.

So unless instructed otherwise, we accept the non-integer.

✔ Answer: 9.6 (or $ \frac{48}{5} $)

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5. The temperature recorded in New York City on Monday is 20°C. If the temperature increases by 10°C on Tuesday and falls by 15°C on Wednesday, find the temperature recorded on Wednesday.

- Monday: $ 20^\circ C $
- Tuesday: $ 20 + 10 = 30^\circ C $
- Wednesday: $ 30 - 15 = 15^\circ C $

✔ Answer: 15°C

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✔ Final Answers:

1. $18
2. 1920 feet
3. Our team won by 2 goals
4. 9.6 (or $ \frac{48}{5} $)
5. 15°C

Let me know if you'd like these answers filled into the worksheet format!