Integer Word Problems Practice worksheet from Math Monks, featuring five real-world scenarios requiring integer operations.

Let’s solve each of the 5 integer word problems step by step.

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Problem 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?

Solution:

Benny only has $75 but the gift costs $93.

So, he needs to borrow:
$93 – $75 = $18

✔ Answer: $18

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Problem 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?

Solution:

- Mountain top: +1270 ft (above sea level)
- Valley bottom: –650 ft (below sea level)

To find the vertical distance between them, subtract the lower elevation from the higher one:

1270 – (–650) = 1270 + 650 = 1920 feet

✔ Answer: 1920 feet

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Problem 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?

Solution:

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

Our team wins by:
5 – 3 = 2 goals

✔ Answer: Our team won by 2 goals

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Problem 4:

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

Solution:

Let the number be x.

Twice the number: 2x
Half of the number: (1/2)x

Equation:
2x + (1/2)x = 24

Combine like terms:
(5/2)x = 24

Multiply both sides by 2:
5x = 48

Divide by 5:
x = 48/5 = 9.6

But wait — the worksheet says “Integer Word Problems”. 9.6 is not an integer.

Let’s double-check the problem.

Is it possible the problem meant “twice a number added to half of itself equals 24” — and expects an integer? Then maybe we made a mistake.

Wait — perhaps the phrasing is ambiguous.

Alternative interpretation: Maybe it means “twice a number, added to half of itself” — which is exactly what we did.

But 48/5 = 9.6 is correct mathematically.

However, since this is an *integer* word problem worksheet, let’s check if there’s a typo or misinterpretation.

Perhaps it meant: “Twice a number, plus half of that number, equals 24” — same thing.

Or maybe: “Twice a number added to half of itself” — still same.

Alternatively, perhaps the problem meant: “Twice a number added to half of *another* number”? But no, it says “itself”.

So unless the problem allows non-integers (which contradicts the title), maybe it’s a trick or error.

But let’s assume the problem is correct as written.

We can write it as:

2x + 0.5x = 24 → 2.5x = 24 → x = 24 / 2.5 = 9.6

Still 9.6.

Wait — maybe the problem meant “twice a number added to half of itself” — and we’re supposed to express as fraction?

But 9.6 = 48/5 — not integer.

Hmm.

Alternatively, perhaps the problem meant: “Twice a number added to half of itself equals 24” — and we are to find the integer closest? But that doesn’t make sense.

Wait — maybe I misread.

Let me re-read: “Twice a number added to half of itself equals 24.”

That is unambiguously: 2x + (1/2)x = 24 → (5/2)x = 24 → x = 48/5 = 9.6

But since this is an *integer* worksheet, perhaps the intended problem was:

“Twice a number added to half of itself equals 25” → then x=10.

Or “equals 20” → x=8.

But as written, it’s 24.

Alternatively, maybe “added to half of itself” means something else?

No — standard interpretation is correct.

Given that, and since the problem says “find the number”, and doesn’t specify integer answer, perhaps it’s acceptable.

But to stay true to the worksheet title, maybe there’s a mistake.

Wait — perhaps the problem is: “Twice a number added to half of itself equals 24” — and we are to solve it, even if not integer.

In many curricula, “integer word problems” might include problems that result in fractions, but involve integers in setup.

Actually, let’s check: the number itself doesn’t have to be integer — the operations involve integers.

The problem says “integer word problems”, which usually means the context involves integers (money, goals, feet, temperature), but the unknown might not be integer.

In this case, the equation involves fractions, so the answer is fractional.

But let’s see if we can interpret differently.

Another possibility: “Twice a number added to half of itself” — maybe they mean (2x) + (x/2) = 24 — same as before.

I think we have to go with 9.6.

But perhaps write it as a fraction.

✔ Answer: 48/5 or 9.6

But since the worksheet likely expects a boxed answer, and it's a practice sheet, maybe they expect 9.6 or 48/5.

Alternatively, perhaps the problem is misprinted, and it should be 25 instead of 24.

If it were 25: 2x + 0.5x = 25 → 2.5x=25 → x=10 — integer.

But as written, it’s 24.

I’ll go with the mathematical answer.

✔ Final Answer: 9.6 (or \frac{48}{5})

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Problem 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.

Solution:

- Monday: 20°C
- Tuesday: 20 + 10 = 30°C
- Wednesday: 30 – 15 = 15°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

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Note for Problem 4: Since this is labeled "Integer Word Problems", and 9.6 is not an integer, there may be a typo in the problem. If the total was 25 instead of 24, the answer would be 10 (an integer). But based on the given text, 9.6 is correct.