# System of equations - math word problems

1. Alcohol mixture
From 55% and 80% alcohol we have to produce 0.2 kg of 60% alcohol. How many of them do we use in solution?
2. Sawmill factory
Peter works in the factory. The bus stop is 10 km from the factory. Therefore, always when the bus arrives for Peter, the driver leaves factory and takes him to work. They are coming at the saw exactly at 8:00. Today the bus arrived 11 minutes earlier and
3. CuZn
Brass is an alloy of copper and zinc. The 10 centimeter brass cube has a weight of 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m3. Calculate how many kg of copper and zinc a cube contains.
4. Magic number
The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
5. Rectangle
The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
6. Pears
Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears.
7. Enterprise company
30% of all employees in the enterprise are women. Men are 360 more. How many employees are in the company?
8. Motel
Three different dinners A, B, C are served in the motel. Three 20 members went to motel. Group 1 ordered dinners: A 20 members and their average dinner price in the group was CZK 200. From Group 2, they ordered a A: 10 persons, B 10 dinners, and their ave
9. Donuts
In the dining room at one table sit Thomas, Filip and Martin. Together they eat 36 donuts. How many donuts eaten everyone, when Filip ate twice as much as Thomas and Martin even half over Filip?
10. Siblings
Three siblings had saved up a total of 1,274 CZK. Peter had saved up to 15% more than Jirka and Hanka 10% less than Peter. How much money they saved each one of them?
11. Concentration
How many grams of 65% and 50% acid is to be mixed to give 240 g acid with a concentration of 60%?
12. Rectangle vs square
One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle.
13. Solution
What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
14. AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
15. Contestants
In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contestan
16. Two numbers
The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.
17. Pupils at cinema
Alena bought movie tickets for two groups of pupils. The first group purchased 7 tickets for 1st and 5 tickets for 2nd place and she pay 62Kč. For the second group bought 11 tickets for 1st and 4 tickets for 2nd place and pay 82Kč. How much was the ticket
18. Car
Car goes some distance in 3 hours and 20 minutes. If it increase speed by 10 km/h, i goes this distance in 2.5 hours. Calculate the distance.
19. Glass
Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will c
20. Three figures - numbers
The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures.

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