Let’s go through each problem one by one. I’ll explain how to write the algebraic expression for each situation, step by step.
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1. Bear Population:
- Starts at p bears.
- Increases by 10% each year → that means multiply by 1.10 every year.
- After t years: you multiply p by 1.10, t times.
→ Expression:
p × (1.10)^t
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2. Bear Cubs:
- She has 3 cubs every 2 years.
- In n years, how many sets of 2 years are there? → n ÷ 2
- Each set gives 3 cubs → so total cubs = 3 × (n/2)
→ Expression:
(3n)/2 or
1.5n
*(Note: If n is odd, she hasn’t had a full litter yet — but since we’re writing an algebraic expression, we assume it works for any n.)*
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3. Food Consumption:
- Eats 5 pounds per day.
- Hibernates for d days.
→ Total food = 5 × d
→ Expression:
5d
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4. Bear Weight:
- Starts at w kilograms.
- Gains 2 kg every month.
- After m months → gains 2 × m kg.
→ New weight = starting weight + gain
→ Expression:
w + 2m
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5. Speed:
- Distance = d, Time = t hours.
- Speed = distance ÷ time
→ Equation:
s = d/t
*(This is the standard speed formula.)*
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6. Bear Tracking:
- Position equation: s = 2t² - 5t + 10
- Find position at t = 3.
→ Plug in t=3:
s = 2*(3)² - 5*(3) + 10
s = 2*9 - 15 + 10
s = 18 - 15 + 10
s = 3 + 10 =
13
→ Answer:
13
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7. Bear Lifespan:
- Cub’s age = c
- Bear lives 15 years longer than twice the cub’s age.
→ Twice cub’s age = 2c
→ Add 15 → 2c + 15
→ Expression:
2c + 15
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8. Conservation Area:
- Square area = 64 km²
- Side length = L
- Area of square = L × L = L²
→ So: L² = 64
→ But they want an equation representing L → just write:
→ Equation:
L² = 64
*(You could solve it: L = 8, but the question asks for the equation, not the value.)*
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9. Fishing:
- Catches 5 fish per hour.
- Fishes for h hours.
→ Total fish = 5 × h
→ Expression:
5h
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10. Migration:
- Distance between habitats = s kilometers.
- Speed = v km/hour.
- Time = distance ÷ speed
→ Expression:
s/v
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Now let me double-check all answers quickly:
1. p*(1.1)^t
✔
2. 3n/2
✔
3. 5d
✔
4. w + 2m
✔
5. s = d/t
✔
6. At t=3: 2*9=18, -5*3=-15, +10 → 18-15=3+10=13
✔
7. 2c + 15
✔
8. L² = 64
✔
9. 5h
✔
10. s/v
✔
All correct!
Final Answer:
1. p(1.10)^t
2. (3n)/2
3. 5d
4. w + 2m
5. s = d/t
6. 13
7. 2c + 15
8. L² = 64
9. 5h
10. s/v
Parent Tip: Review the logic above to help your child master the concept of substitution word problems worksheet.
