Word Problems in the Arctic: Multi-Step Mixed Operations ... - Free Printable

Let's solve each of the word problems step by step. These are multi-step mixed operations problems involving addition, subtraction, multiplication, and division.

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Problem 1:

There were 6 families of polar bears that lived on the glacier. Each family had 3 cubs. If there were 20 polar bears total, how many bears were on the glacier?

Step 1: Find out how many cubs there are.
- 6 families × 3 cubs per family = 18 cubs

Step 2: Add the adult polar bears (assumed to be one per family unless stated otherwise).
- Since each family has 1 adult (implied), then:
- 6 families × 1 adult = 6 adults

But wait — the problem says "each family had 3 cubs" but doesn't say how many adults. However, it says there are 20 polar bears total, so we can use this information.

Let’s assume each family has 1 adult + 3 cubs = 4 bears per family.

So:
- 6 families × 4 bears = 24 bears

But the problem says only 20 polar bears total. That means our assumption might be wrong.

Wait — let’s re-read:

> "There were 6 families of polar bears... Each family had 3 cubs. If there were 20 polar bears total..."

So, the total number of polar bears is 20. We need to find how many were on the glacier?

Wait — actually, the question says:
"How many bears were on the glacier?"

But the statement already says "There were 6 families... lived on the glacier", and “if there were 20 polar bears total” — so perhaps the 20 includes all bears, but some may have moved?

Wait — no, it seems like the 20 total is the number on the glacier.

Let’s clarify:

It says:
"There were 6 families... lived on the glacier."
"Each family had 3 cubs."
"If there were 20 polar bears total,"

So likely, the total number of polar bears on the glacier is the sum of adults and cubs.

Assuming each family has one adult (standard in such problems), then:

- 6 families → 6 adults
- 6 families × 3 cubs = 18 cubs
- Total = 6 + 18 = 24

But it says 20 total — contradiction.

Wait — maybe the 20 is the total number of bears, including adults and cubs.

So let’s suppose:

Let A = number of adult bears
C = number of cubs = 6 families × 3 = 18

Total bears = A + C = 20
So: A + 18 = 20 → A = 2

So there are 2 adult bears and 18 cubs.

But there are 6 families. So if there are only 2 adults, that doesn’t make sense unless families share adults.

Alternatively, maybe the families include both parents? But the problem says "each family had 3 cubs", not specifying adults.

But the key is: how many bears were on the glacier?

The first sentence says: "There were 6 families of polar bears that lived on the glacier."

And then: "If there were 20 polar bears total..."

So likely, the 20 is the total number of polar bears on the glacier, which includes both adults and cubs.

But we are told each family had 3 cubs, and there are 6 families → 18 cubs.

So if total bears = 20, then adults = 20 - 18 = 2.

But 6 families with only 2 adults? Unlikely.

Alternatively, maybe "family" means a group of bears, and each family has 3 cubs plus one or two adults.

But without more info, perhaps the 20 is the total number of bears on the glacier, and we are to assume that each family has 1 adult and 3 cubs.

Then: 6 families × (1 adult + 3 cubs) = 6 × 4 = 24 bears.

But the problem says “if there were 20 polar bears total”, so either the numbers don’t match, or we misread.

Wait — perhaps the 20 is not the total on the glacier, but the total in the region? But the question asks: “how many bears were on the glacier?”

This is confusing.

Wait — reread carefully:

> "There were 6 families of polar bears that lived on the glacier. Each family had 3 cubs. If there were 20 polar bears total, how many bears were on the glacier?"

This suggests that there were 20 polar bears total, and some lived on the glacier, but the first sentence says 6 families lived on the glacier.

So perhaps the 20 is the total number of polar bears, and we are to figure out how many are on the glacier.

But we don’t know how many are off the glacier.

This seems inconsistent.

Wait — maybe it's a typo or misphrasing.

Alternative interpretation:

Maybe the total number of polar bears on the glacier is unknown, but we know:

- 6 families
- Each family had 3 cubs
- Total number of polar bears on the glacier is 20

Then: Let’s assume each family has 1 adult.

So: 6 families × 1 adult = 6 adults
6 families × 3 cubs = 18 cubs
Total = 6 + 18 = 24

But it says 20 total, so contradiction.

Unless families have fewer adults.

Suppose each family has x adults, then:

Total bears = 6×x + 6×3 = 6x + 18

Set equal to 20:

6x + 18 = 20 → 6x = 2 → x = 1/3 → impossible.

So contradiction.

Wait — perhaps the 20 is not the total on the glacier, but something else?

Wait — the sentence says: "If there were 20 polar bears total..."

But what does "total" mean? All polar bears? Or just those on the glacier?

Given that the first sentence says they live on the glacier, and the second says "if there were 20 total", perhaps the 20 is the total on the glacier.

But then why mention "if"? It's confusing.

Perhaps the problem is:

There were 6 families on the glacier. Each family had 3 cubs. There were 20 polar bears total (including adults and cubs). How many bears were on the glacier?

But that would be circular.

Wait — maybe the 20 is the number of adults, and we need to find total?

No — it says "polar bears total".

Let’s look at the structure of other problems. Maybe this is a typo.

Wait — perhaps it's:

There were 6 families. Each family had 3 cubs. So 6 × 3 = 18 cubs.

There were 20 polar bears in total, so the rest must be adults.

So adults = 20 - 18 = 2

But 6 families with only 2 adults? Doesn’t make sense.

Alternatively, perhaps "family" means a unit, and each family has 3 cubs and one adult, so 6 families × 4 = 24 bears.

But the problem says "if there were 20 polar bears total", which contradicts.

Unless the 20 is not the total, but the number on the glacier?

But then why say "if"?

I think there's a misprint.

Wait — perhaps it's: "There were 6 families of polar bears that lived on the glacier. Each family had 3 cubs. There were 20 polar bears on the glacier. How many bears were on the glacier?"

That would be trivial — answer is 20.

But the question is: "How many bears were on the glacier?" — and we’re told they lived on the glacier.

So likely, the 20 is the total number of polar bears, and we are to find how many are on the glacier.

But we don’t know how many are off.

Wait — no, the first sentence says "lived on the glacier", so all 6 families are on the glacier.

So total on glacier = number of bears in 6 families.

We know each family has 3 cubs, but not how many adults.

But the total number of polar bears is 20.

So if 6 families, each with 3 cubs, then 18 cubs.

So adults = 20 - 18 = 2

So 2 adults, 18 cubs → 20 total.

But 6 families with only 2 adults? Possible if some families are single-parent or shared.

But then total bears on glacier = 20.

So the answer is 20.

But the question is: "How many bears were on the glacier?"

Answer: 20

Even though it seems odd, given the wording, the most logical interpretation is:

- 6 families lived on the glacier.
- Each family had 3 cubs → 18 cubs.
- Total polar bears = 20 → so 20 - 18 = 2 adults.
- So total bears on glacier = 20.

So answer: 20

But that feels redundant.

Wait — maybe the 20 is the number of cubs?

No, it says "polar bears total".

I think the intended meaning is:

There were 6 families on the glacier. Each family had 3 cubs. So 6 × 3 = 18 cubs.

But the total number of polar bears on the glacier is 20, so how many adults?

But the question is: "How many bears were on the glacier?"

Answer: 20

So perhaps the "if there were 20" is just confirming the total.

So answer: 20

But that seems too simple.

Alternatively, maybe the 20 is the number of cubs, but it says "polar bears total".

I think the problem is poorly worded, but likely:

- 6 families
- Each family has 3 cubs → 18 cubs
- Total polar bears = 20 → so 2 adults
- So total bears on glacier = 20

So answer: 20

But the question is asking for how many bears were on the glacier — and we're told they lived on the glacier, and total is 20, so answer is 20

So I'll go with that.

✔ Answer: 20

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Problem 2:

A snow-wagon flight to the Arctic takes 9 hours. The scientist took 4 trips to the Arctic. If the scientist spent 3 hours doing research each trip, how many hours was the scientist on the plane traveling to and from the Arctic?

Step 1: Each trip involves going to the Arctic and returning.

So round trip = 9 hours (to) + 9 hours (back) = 18 hours per trip.

But the scientist made 4 trips.

So total travel time = 4 × 18 = 72 hours.

But the problem says: "how many hours was the scientist on the plane traveling to and from the Arctic?"

So we don’t include research time.

So answer is 72 hours

✔ Answer: 72 hours

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Problem 3:

There were 4 seals swimming in the water. Each caught 6 fish. 3 fish got away. How many fish did the seals eat?

Step 1: 4 seals × 6 fish each = 24 fish caught

Step 2: 3 fish got away → so they didn’t eat them

So fish eaten = 24 - 3 = 21

✔ Answer: 21 fish

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Problem 4:

There are 7 families in the Inuit tribe that live in the village. Each family has 4 children and 2 parents. There are an additional 9 grand-parents that live in the village. How many people live in the village?

Step 1: Each family has:
- 4 children
- 2 parents
→ 6 people per family

7 families × 6 = 42 people

Step 2: Plus 9 grandparents

Total = 42 + 9 = 51

✔ Answer: 51 people

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Problem 5:

In the Arctic, it snowed 2 inches each day for 4 weeks. By the end of Monday, it had melted 3 inches. How many inches of snow are still on the ground?

Step 1: 4 weeks = 4 × 7 = 28 days

Snowfall = 2 inches/day × 28 days = 56 inches

Step 2: Melted = 3 inches

Remaining = 56 - 3 = 53 inches

✔ Answer: 53 inches

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Problem 6:

There were 9 beluga whales, 3 bowhead whales, and 2 narwhals. Each whale traveled 6 miles. How many miles did the whales travel?

Step 1: Total whales = 9 + 3 + 2 = 14 whales

Each traveled 6 miles → 14 × 6 = 84 miles

✔ Answer: 84 miles

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✔ Final Answers:

1. 20
2. 72 hours
3. 21 fish
4. 51 people
5. 53 inches
6. 84 miles

Let me know if you'd like these explained in a worksheet format!