# System of equations - examples - page 27

1. Mixing water The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix?
2. New ratio The ratio of ducks and chicken in our yard is 2 : 3. The total number of ducks and chickens together is 30. Mother gave 3 of the chickens to our neighbor. What is the new ratio now?
3. Barrel with water The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
4. Beds At the summer camp, there are 41 chalets. Some rooms are 3-beds, some 4-beds. How many campers from 140 are living in 3-bed?
5. Square into three rectangles Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
6. Integer Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
7. Simple equations Solve system of equations: 5x+3y=5 5x+7y=25
8. Company and employees There are 370 employees in the company - women are 15% less than men. How many men work in the company?
9. 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?
10. 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 m
11. Grandfather and grandmother The old mother is 5 years younger than the old father. Together they are 153 years old. How many years has each of them?
12. Sheep and cows There are only sheep and cows on the farm. Sheep is eight more than cows. The number of cows is half the number of sheep. How many animals live on the farm?
13. 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?
14. Three sides Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
15. The tourist The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus gone?
16. Two trains There were 159 freight wagons on the railway station creating 2 trains. One had 15 more wagons than the other. How many wagons did each train have?
17. Car and motorcyclist A car and a motorcyclist rode against each other from a distance of 190 km. The car drove 10km/h higher than the motorcyclist and started half an hour later. It met a motorcyclist in an hour and thirty minutes. Determine their speeds.
18. Substitution solve equations by substitution: x+y= 11 y=5x-25
19. Stamps 2 Dennis spent 34.15 on stamps. The number of .56 is 10 less than four times of stamps bought for .41. How many of each stamp did he buy?
20. The larger The larger of two numbers is nine more than four times the smaller number. The sum of the two numbers is fifty-nine. Find the two numbers.

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