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1. Learning Objectives
- Translate real-life scenarios into mathematical inequalities.
- Solve word problems involving budgets, limits, and geometry.
- Interpret solutions within a practical context.
2. Translation Guide
Look for these keywords to choose the correct symbol:
- ≥ : "At least", "Minimum", "No less than"
- ≤ : "At most", "Maximum", "No more than"
- > : "More than", "Exceeds"
- < : "Less than", "Below"
Click the button below each question to reveal the explanation.
1. You have 200 Birr. A notebook costs 25 Birr. Write an inequality for the number of notebooks (n) you can buy.
Cost cannot exceed budget. 25n ≤ 200. Divide by 25: n ≤ 8. Ans: n ≤ 8
2. A car rental costs 500 Birr plus 2 Birr per km. If you want to spend at most 1000 Birr, find the distance (d).
500 + 2d ≤ 1000 → 2d ≤ 500 → d ≤ 250. Ans: d ≤ 250 km
3. The sum of two consecutive integers is more than 50. Find the smallest possible integer.
x + (x + 1) > 50 → 2x + 1 > 50 → 2x > 49 → x > 24.5. Next integer is 25. Ans: 25
4. A rectangle's length is 10m. The area must be at least 50m². Find the width (w).
10w ≥ 50 → w ≥ 5. Ans: w ≥ 5m
5. To pass a course, the average of two tests must be at least 70. You got 65 on the first test. What score (s) do you need on the second?
(65 + s)/2 ≥ 70 → 65 + s ≥ 140 → s ≥ 75. Ans: s ≥ 75
6. A phone plan costs 30 Birr/month plus 0.50 Birr/min. If your budget is less than 60 Birr, how many minutes (m) can you talk?
30 + 0.5m < 60 → 0.5m < 30 → m < 60. Ans: m < 60 mins
7. Twice a number increased by 10 is at most 40. Find the number.
2x + 10 ≤ 40 → 2x ≤ 30 → x ≤ 15. Ans: x ≤ 15
8. A triangle has sides 5, 8, and x. According to the Triangle Inequality, what must be the range of x?
Sum of two sides > third side. 8-5 < x < 8+5. Ans: 3 < x < 13
9. A theater holds maximum 500 people. If 120 children are present, how many adults (a) can enter?
a + 120 ≤ 500 → a ≤ 380. Ans: a ≤ 380
10. If you triple your savings (s) and subtract 100, you have more than 500 Birr. Find s.
3s - 100 > 500 → 3s > 600 → s > 200. Ans: s > 200 Birr
11. A lift can carry at most 800kg. If the operator weighs 80kg, how much cargo (c) can be loaded?
c + 80 ≤ 800 → c ≤ 720. Ans: c ≤ 720kg
12. A number decreased by 5 is no more than -2. Find the range.
x - 5 ≤ -2 → x ≤ 3. Ans: x ≤ 3
13. The perimeter of a rectangle is less than 40cm. If width is 8cm, what is the range of length (L)?
2(L + 8) < 40 → L + 8 < 20 → L < 12. Also, L must be > 0. Ans: 0 < L < 12
14. You need to earn at least 1500 Birr/week. You earn 150 Birr/hour. How many hours (h) must you work?
150h ≥ 1500 → h ≥ 10. Ans: h ≥ 10 hours
15. A number divided by 4 is at least -2. Find the range.
x/4 ≥ -2 → x ≥ -8. Ans: x ≥ -8
16. Five times a number is less than 3 times that number plus 10. Solve.
5x < 3x + 10 → 2x < 10 → x < 5. Ans: x < 5
17. A company's profit (P) must exceed 20,000 Birr. If revenue is 50,000, write an inequality for expenses (E).
50,000 - E > 20,000 → -E > -30,000 → E < 30,000. Ans: E < 30,000 Birr
18. Three consecutive odd integers have a sum at most 57. Find the largest possible first integer.
x + (x+2) + (x+4) ≤ 57 → 3x + 6 ≤ 57 → 3x ≤ 51 → x ≤ 17. Ans: 17
19. If a temperature (T) in Celsius is between 15 and 25, write it.
Compound inequality. Ans: 15 < T < 25
20. A park charges 5 Birr entry plus 10 Birr per ride. How many rides (r) can you take with 35 Birr?
5 + 10r ≤ 35 → 10r ≤ 30 → r ≤ 3. Ans: r ≤ 3 rides