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Math Exercises: Equation Word Problems





1. The tourists are accommodated in 3 hotels. There are 8 more tourists in the second hotel than in the first hotel and in the third hotel there are 14 more tourists than in the second one. If there is a total of 258 tourists, how many tourists are accommodated in each of the hotels ?


2. Sisters Jane and Dane have saved 220 € in total. They are going on the trip and Jane wants to take fifth of her savings and Dane wants to take quarter of hers. If they do so, they will have 50 € together. How many euros have saved each one of them ?


3. Numerator of the fraction is 2 less then denominator. If we lower the numerator of this fraction by one and we increase denominator by 3, the fraction shall be equal ¼. Determine the fraction.


4. Three painters are supposed to paint the bridge. The first one would get this work done in 5 days, the second one in 6 days and the third one in 7.5 days. How long will it take to paint the bridge, if they will work together ?


5. The factory has 1,440 employees (men and women). For above-avarage results 18.75% of all men and 22.5% of all women received the bonus. The total amount of awarded employees is 20% . How many women and how many men are employed in the factory ?


6. A local train has departed from the station A at ten o'clock with the speed of 55 km/h. One and a half of an hour later an express has departed from the station B, which is 360 km far from the station A, and it went toward the local train with the speed of 130 km/h. At what time and how far from the station A will the two trains meet ?


7. The length of the rectangle is 12 cm bigger than three its widths. Perimether of the rectangle is 104 cm. What are the lengths of the sides ?


8. The distance between towns A and B is 42 km. A pedestrian leaves town A with a speed of 6 km/h, to the opposite direction from town B. A cyclist leaves town B half an hour later than the pedestrian with a speed of 24 km/h. In how many hours is the cyclist going to reach the pedestrian and what is going to be his distance from town B ?


9. There are 51 students accommodated in 15 rooms. Some of the rooms are 4-bed bedrooms and the rest of them are 3-bed bedrooms. How many of them are 4-bed bedrooms and how many of them are 3-bed bedrooms, if two beds in dormitory are free ?


10. Surfaces of two cubes differ by 19,272 cm2. One of them has longer edge by 22 cm then the other. Calculate the lenght of the edges of both cubes.


11. Sea water contains 5% of salt. How many kg of fresh water we need to add to 40 kg of sea water to reduce the salt content to 2% ?


12. The water dam is filled up using the first tributary in 1 hour and 10 minutes, using the second tributary in 60 minutes. How many minutes it takes to fill the half of the dam using both of the tributaries, if the second tributary will be opened 12 minutes after the first one ?


13. One tractor driver would plow the field in 15 hours, the second tractor driver, with a more powerful machine, would do the same job in 12 hours. In what time do they plow the field together, if the second tractor driver starts plowing 2 hours later than the first one ?


14. The father is 48 years old and he has 21 years old son. How many years ago has father been 10 times older than his son ?


15. After the first ride, car consumed 20% of the fuel in the tank. After the second ride, car consumed 10% of amount remaining after the first trip. After the two rides, 9 liters of fuel was left in the tank. How many liters of fuel was initially in the tank ?


16. The workshop purchased 40 pieces of garden tools. Spades cost 16 € each and hoes cost 18 € each. The price of all tools together was 690 €. Calculate how many spades and how many hoes did the workshop purchase.


17. Half of the students from the ninth grade wants to study on secondary technical school, a quarter of them on the secondary vocational schools, one sixth on grammar schools and three students do not want to continue their studies. How many students are in the class ?


18. Calculate the side length of a square and the side lengths of a rectangle, if one side of the rectangle is 5 cm longer than the side of the square and the other side of the rectangle is 2 cm shorter than the side of the square. The area of the rectangle is 11 cm2 bigger than the area of the square.


19. Fast train gets from the starting to the final station in 4 hours and 20 minutes. The slower local train, whose average speed is 30 km/h lower, is able to make the same journey in 7 hours and 40 minutes. What is the speed of the fast train and what is the speed of the local train ?


20. The school cafeteria for 141 boarders is supposed to buy two types of desserts worth 300 euros overall. Cheaper dessert costs 2 euros and the expensive one cost 2.50 euros. How many desserts do they need to buy from each type ?


21. A square and a rectangle have the same areas. The length of the rectangle is longer by 9 than the side of the square. The width of the rectangle is shorter by 6 than the side of the square. Calculate the side length of the square.


22. The length of the lot is 8 m shorter than three times its width. If we increase its width by 5% of the length and we decrease the length by 14% of its width, the perimeter of the lot will increase by 30 m. What are the length and the width of the lot ?


23. The sum of squares of two consecutive natural numbers is 1,201. Identify both of the numbers.


24. The rectangle has a perimeter of 28 cm and a diagonal length of 10 cm. Determine the dimensions of the rectangle.


25. The sum of the nominator and denominator of an unknown fraction is 49. The ratio of this fraction to its reciprocal fraction is 9:16. Identify the unknown fraction.


26. How many percent of the Earth's surface would be covered by the surface of the Moon, if the radius of the Earth is 6,378 km and the radius of the Moon is 1,741 km ?


27. A right-angled triangle, whose legs are in the ratio 5:12, has the hypotenuse 26 cm long. What is the length of the legs ?


28. The front wheel of a vehicle has a perimeter of 2.1 m, and the back wheel perimeter is 3.5 m. What is the length of a track, on which the back wheel spins 2,000 less times than the front wheel ?


29. The hypotenuse of a right-angled triangle is 17 cm long. If we reduce both legs by 3 cm, the hypotenuse reduces by 4 cm. Determine the length of both legs.


30. Which regular polygon has 42 more diagonals than it has sides ?







You might be also interested in:

- Inequality Word Problems

- Unit Conversion Word Problems

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- Linear Equations and Inequalities

- Systems of Equations and Inequalities

- Quadratic Equations and Inequalities

- Irrational Equations and Inequalities

- Exponential Equations and Inequalities

- Logarithmic Equations and Inequalities

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- Complex Numbers and Equations

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