Algebra Word Problems Worksheets - 15 Worksheets Library - Free Printable

Here's the solution to all 10 problems from the “Bears” worksheet, with clear explanations for each:

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1. Bear Population:
*The population of bears in a national park is currently p and is increasing by 10% each year. Write an algebraic expression for the population of bears after t years.*

✔ Expression: `p × (1.10)^t` or `p × (1 + 0.10)^t`

🔹 Explanation:
A 10% increase means each year the population is multiplied by 1.10 (since 100% + 10% = 110% = 1.10). After t years, this happens t times, so we raise 1.10 to the power of t and multiply by the original population p.

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2. Bear Cubs:
*A female bear gives birth to 3 cubs every 2 years. If the number of cubs in the first year is 6, write an algebraic expression for the number of cubs after n years.*

✔ Expression: `6 + 3 × (n ÷ 2)` → Simplified: `6 + (3n)/2`

🔹 Explanation:
She gives birth to 3 cubs every 2 years. So in n years, she gives birth `n/2` times (assuming n is even or we’re allowing fractional births for modeling). Starting with 6 cubs, we add 3 for each 2-year interval: 6 + 3×(n/2).

> Note: If the problem implies that births only happen at full 2-year intervals, you might use floor(n/2), but since it’s an algebraic expression without specifying integer constraints, `(3n)/2` is acceptable.

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3. Food Consumption:
*A bear consumes 5 pounds of food per day. If the bear has been hibernating for 3 days, write an algebraic expression for the total amount of food consumed during hibernation.*

✔ Expression: `5 × 3 = 15` — but since it asks for an *expression*, we can write: `5 × d`, where d = days hibernating.

But the problem says “for 3 days”, so it’s fixed.

✔ Final Expression: `5 × 3` or simply `15`

🔹 Explanation:
The bear eats 5 pounds per day. For 3 days, total consumption = 5 × 3 = 15 pounds. Since the number of days is given as 3 (not variable), the expression is just `15`. However, if we were to generalize for d days, it would be `5d`.

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4. Bear Weight:
*A bear weighs w kilograms. If the bear gains 2 kilograms per month for m months, write an algebraic expression for the bear’s weight after m months.*

✔ Expression: `w + 2m`

🔹 Explanation:
Starting weight is w. Each month, it gains 2 kg. After m months, it gains `2 × m` kg. Total weight = starting weight + gain = `w + 2m`.

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5. Speed:
*A bear is running at a constant speed. If the distance traveled by the bear is d kilometers and the time taken is t hours, write an algebraic expression relating the speed, distance, and time.*

✔ Expression: `s = d / t`

🔹 Explanation:
Speed (s) equals distance (d) divided by time (t). This is the standard formula: `speed = distance ÷ time`.

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6. Bear Tracking:
*A group of researchers is tracking the movement of bears in a forest. The position of a bear at time t is given by the equation p = 2t² + 5t + 10, where p is the position in kilometers. Find the position of the bear at t = 3.*

✔ Expression (value): Plug t = 3 into the equation:

`p = 2(3)² + 5(3) + 10 = 2(9) + 15 + 10 = 18 + 15 + 10 = 43`

✔ Answer: `43 kilometers`

🔹 Explanation:
Substitute t = 3 into the given quadratic equation and compute step by step.

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7. Bear Lifespan:
*The lifespan of a bear is 15 years longer than twice the age of a cub. If the age of a cub is c years, write an algebraic expression for the lifespan of a bear.*

✔ Expression: `2c + 15`

🔹 Explanation:
Twice the age of a cub = `2c`. Add 15 years → `2c + 15`.

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8. Conservation Area:
*A square bear conservation area has an area of 64 square kilometers. Write an algebraic equation to represent the length, L kilometers, of one side of the conservation area.*

✔ Equation: `L² = 64`

🔹 Explanation:
Area of a square = side × side = L². Given area is 64, so `L² = 64`. You could also solve for L: `L = √64 = 8`, but the question asks for the *equation*, not the solution.

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9. Fishing:
*A bear catches 5 fish every hour. If the bear has been fishing for h hours, write an algebraic expression for the total number of fish caught.*

✔ Expression: `5h`

🔹 Explanation:
Rate is 5 fish/hour. Over h hours, total fish = rate × time = `5 × h = 5h`.

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10. Migration:
*A group of bears migrates from their summer habitat to their winter habitat. If the distance between the two habitats is d kilometers and the bears travel at a speed of s kilometers per hour, write an algebraic expression for the time taken to migrate.*

✔ Expression: `t = d / s`

🔹 Explanation:
Time = Distance ÷ Speed. So, `time = d / s`.

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## ✔ Final Answer Summary:

1. `p × (1.10)^t`
2. `6 + (3n)/2`
3. `15` (or `5 × 3`)
4. `w + 2m`
5. `s = d / t`
6. `43`
7. `2c + 15`
8. `L² = 64`
9. `5h`
10. `d / s`

Let me know if you’d like these formatted as a printable answer key! 🐻