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1. Learning Objectives
- Translate real-world word problems into mathematical equations.
- Solve problems related to numbers, ages, geometry, and finance.
- Interpret the mathematical results in the context of the original problem.
2. Problem Solving Steps
- Identify: What is the unknown? Assign a variable (e.g., let x = the number).
- Translate: Write the equation based on the keywords (e.g., "sum" means +, "is" means =).
- Solve: Use algebraic methods to find the value of the variable.
- Check: Does the answer make sense in the real world?
Click the button below each question to reveal the explanation.
1. The sum of a number and 15 is 40. Find the number.
Equation: x + 15 = 40. Subtract 15: x = 25. Ans: 25
2. Three times a number decreased by 5 is 16. What is the number?
Equation: 3x - 5 = 16 → 3x = 21 → x = 7. Ans: 7
3. Abebe is 5 years older than Chala. Their total age is 25. How old is Chala?
Let Chala = x, Abebe = x+5. Eq: x + (x+5) = 25 → 2x = 20 → x = 10. Ans: 10
4. The perimeter of a square is 32cm. Find the length of one side.
Eq: 4s = 32 → s = 8. Ans: 8cm
5. Two consecutive integers sum to 21. Find the smaller one.
Eq: x + (x+1) = 21 → 2x = 20 → x = 10. Ans: 10
6. A rectangle's length is twice its width. Perimeter is 30m. Find width.
Let w=width, l=2w. Eq: 2(2w + w) = 30 → 6w = 30 → w = 5. Ans: 5m
7. A pen and notebook cost 50 Birr. The notebook is 10 Birr more than the pen. Find pen cost.
p + (p+10) = 50 → 2p = 40 → p = 20. Ans: 20 Birr
8. Half of a number is 14. Find the number.
x/2 = 14 → x = 28. Ans: 28
9. A farmer has chickens and cows. Total heads = 10, total legs = 32. How many cows?
Let c=cows, h=chickens. c+h=10, 4c+2h=32. Solving gives c=6. Ans: 6 cows
10. 20% of a number is 50. What is the number?
0.20x = 50 → x = 50/0.20 = 250. Ans: 250
11. A triangle has angles x, 2x, and 3x. Find x.
x + 2x + 3x = 180 → 6x = 180 → x = 30. Ans: 30°
12. If you double a number and add 8, you get 30. Find it.
2x + 8 = 30 → 2x = 22 → x = 11. Ans: 11
13. A car travels at 60km/h. How long (t) to cover 240km?
Distance = Speed × Time → 240 = 60t → t = 4. Ans: 4 hours
14. The sum of three consecutive integers is 33. Find the middle one.
(x-1) + x + (x+1) = 33 → 3x = 33 → x = 11. Ans: 11
15. A number divided by 4 and increased by 3 is 7. Find it.
x/4 + 3 = 7 → x/4 = 4 → x = 16. Ans: 16
16. The area of a rectangle is 50. Length is 10. Find width.
Area = l × w → 50 = 10w → w = 5. Ans: 5
17. A shirt costs 200 Birr after a 50 Birr discount. Find original price.
x - 50 = 200 → x = 250. Ans: 250 Birr
18. If a number is subtracted from 50, the result is 12. Find it.
50 - x = 12 → x = 38. Ans: 38
19. Five years ago, Sara was 10. How old is she now?
x - 5 = 10 → x = 15. Ans: 15
20. Two angles are supplementary (sum to 180°). One is 20° more than the other. Find the smaller angle.
x + (x + 20) = 180 → 2x = 160 → x = 80. Ans: 80°