# System of equations - math word problems

1. Alfa beta gama
The triangle's an interior angle beta is 10 degrees greater than the angle alpha and gamma angle is three times larger than the beta. Determine the size of the interior angles.
2. Factory and divisions
The factory consists of three auxiliary divisions total 2,406 employees. The second division has 76 employees less than 1st division and 3rd division has 212 employees more than the 2nd. How many employees has each division?
3. Remuneration
Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received?
4. PC disks
Peter has 45 disks in three colors. One-fifth of the disks are blue, red are twice more than the white. How much is blue, red and white disks?
5. ATC camp
The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple?
6. Tour
35 people went on a tour and paid 8530, -. Employees pay 165, and family members 310. How many employees and how many family members went to the tour?
7. Sum of three numbers
The sum of three numbers from which second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine this numbers.
8. Schools
Three schools are attended by 678 pupils. To the first attend 21 students more and to the third 108 fewer students than to second school. How many students attend the schools?
9. Copper parts
From copper cast were made 3 parts. At first consumed one third of casting, the second 2/3 of rest and the third weighed 18 kg. What is the weight of original copper cast?
10. Sweets
We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
11. Summerjob
Three students participated in the summerjob. Altogether they earn 1780, -. Peter got a third less than John and Paul got 100,- more than Peter. How much got every one of them?
12. Sides of triangle
Triangle has circumference 42 cm. Side a is 2 times shorter than side b and sice c is 2 cm longer than side a. Determine the sizes of sides of a triangle.
13. Reward
Three workers have shared a common reward 13110 CZK follows: first worker got 35% less than the second and third worker got 20% more than the second worker. How much got each worker?
14. Two planes
Two planes flying from airports A and B, 420 km distant against each other. Plane from A took off 15 minutes later and flies at an average speed of 40 km/h higher than the plane from B. Determine the average speed of this two aircraft if you know that i
15. Mushrooms
Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
16. Internal angles
Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.
17. Parabola 3
Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
18. Two trains
There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railway
19. The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
20. Rectangle from string
String 12m. Make rectangle when one side is two times longer than its width.

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