# System of equations - math word problems

1. The truck
The empty truck left the warehouse for goods at 10:00 and arrived at 11:30. At 2:00 pm, they loaded back on the same route. But it was a quarter slower than going to the warehouse. We know that on the way to the warehouse, the car was traveling at a speed
2. Ratio of sides
The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
3. A triangle
A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
4. Hotel rooms
In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?
5. Value 4
If 5/18=425 what is the value 13/18?
6. Employees
The company employs 1 440 employees (men and women). For over-average results, the premiums were 18.75% of all men and 22.5% of all women. 20% of employees were rewarded with premiums. How many men and how many women are employed in the company?
7. Alice
Alice spent 5/11 of her money on a back pack. She has \$42 dollars left. How much was her back pack?
8. The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
9. Two equations
Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
10. Soaps
Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma
11. Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
12. A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.
13. 12 apples
12 apples and 2 loaves of bread cost 5.76 and 6 apples and 3 loaves of bread cost 7.68. How much is a loaf of bread?
14. A candle
A candle shop sells scented candles for \$16 each and unscented candles for \$10 each. The shop sells 28 candles today and makes \$400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How
15. Father 7
Father is 6 times older than his son. After 4 years, the father will only be 4 times older. What are their present ages?
16. 13 tickets
A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour?
17. Perimeter of a rectangle
If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width?
18. Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
19. Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
20. Father and son
When I was 11, my father was 35 years old. Today, my father has three times more years than me. How old is she?

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