# System of equations - examples - page 23

1. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
2. Geometric seq
Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
3. Potatoes bags
I have three bags with 21 kg potatoes. The first bag is 5.5 kg more than in the second bag and the third is 0.5 kg more than in the second bag. Determine how many kgs of potatoes is in each bag.
4. ATC camp
The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple?
5. 925 USD
Four classmates saved an annual total 925 USD. The second save twice as the first, third 35 USD more than the second and fourth 10 USD less than the first. How USD save each of them?
6. 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?
7. 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?
8. Collecting day
At collecting day at school pupils of three classes took total of 1063 kg of paper. Class B collected half more than A Class and class C 55 kg more than B. How many kg of paper collected each class?
9. Dividing money
Imrich, Daniel and Dezider shared an unknown amount in the ratio 1:2:4, where Dezider received 750 euros more than Imrich and Daniel got half as much as Dezider. Determine an unknown amount of money and determine the amounth that got Imrich, Daniel and De
10. Trees
Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?
11. Three friends
Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor.
12. 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.
13. Three granaries
Three granaries hold 7,800 metric cent (q) of grain. In the first, 70 tonnes of grain was more than the second and in the third it was 120 tonnes less than in the second. How many grain were in each granary?
14. Subjects
Student makes a mathematical task for five minutes and the task from biology in twelve minutes. Another day he have homework in math and biology which consists of eleven tasks together. To do the job took hour and a half. How many tasks maked in each subje
15. Years
Susan is 3 years and as she will be old as Teodor now him will be 11. How old is Teodor today?
16. 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?
17. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
18. MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
19. Savings 2
Jozef and Michael saved 46 euros together. Michael saved 22 euros more than Jozef. How much did save each of them?
20. Distance between two cities
Car went from A to B 4h. On the way back, the car was up 15km / h faster. The return trip took 48 minutes. Shorter than the way there. Find the distance of the cities A and B.

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