# System of equations - math word problems

1. Clouds
From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
2. Angles of a triangle
In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
3. Three piles
100 kg of sugar we divide into three piles. The first pile is small. If we added to second 2 kg of sugar it would have 25% more sugar than the first pile. If we added to third pile 3 kg of sugar it would have 20% more sugar than the 2nd pile. How many kil
4. Bottles
Mrs. Violet brewed 15 l of raspberry juice. She poured it into 17 bottles. Some were 3/4 liter and some one liter. How many was bottles of this two types?
5. Is right triangle
One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
6. Ascent and descent
Car goes 114 km track, which consists of ascent and descent at time of 1 hour 35 minutes. When climbing moves at the speed 48 km/h and downhill 25 m/s. What is the length of climb and descent?
7. Numbers at ratio
The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers?
8. Ring
The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm3. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3
9. Two lands
The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
10. Mother and daughter
The ratio of years mother and daughter is 5:2. After 7 years the ratio is 2: 1. How many years ago daughter was born?
11. Men, women and children
On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
12. Mixing
If we mix 5 kg of goods of one kind and 3 kg second one, resulting mixture cost 16.50 EUR/kg. If these quantities are mixed in reverse - first three kilograms and 5 kilograms second cost of mixture is 18.50 EUR/kg. What is the price of one kg of goods of
13. Two numbers
We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
14. Saving
Paul save 155Kč in 46 2 Kc and 5Kc coins. How much saved 2Kc and 5Kc coins?
15. Bob and Bobek
At 10h 20min runs Bobek from hat at average speed 12 km/h. At what time must run out Bob at speed 18 km/h to catch him 9 kilometers from the hat?
16. Forth and back
Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B?
17. Landlord
Landlord had 49 ducats more than Jurošík. How many ducats Jurošík steal landlord if the Jurošík now 5 ducats more?
18. Two pipes
One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
19. Sebastian
From Kovalov Sebastian walks at 6 km / h started at 8:00 in the direction of Kuty. From Kuty, the godfather is driving at 50 km/h and started at 8:30. The distance is 24 km. When and where grandfather will take Sebastian to the car.
20. Passenger car and truck
From Kutna Hora left at 11:00 clock a truck at 60 km/h. At 12:30 behind him started passenger car at average speed 80 km/h. At what time and how far from Kutna Hora overtake a passenger car truck?

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