# Algebra - problems - page 75

1. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
2. ATC camp
The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple?
3. 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?
4. 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?
5. Bar
Half of the bar is green, the third is yellow and the remaining 40cm is red. How long is a bar?
6. 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?
7. 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
8. Diagonals
Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
9. Cleaning windows
Cleaning company has to wash all the windows of the school. The first day washes one-sixth of the windows of the school, the next day three more windows than the first day and the remaining 18 windows washes on the third day. Calculate how many windows ha
10. Red balls
In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?
11. Two machines
Performances of two machines are in a ratio of 7:12. A machine with less power produced 406 pieces of products per shift. a) How many pieces produced per shift second machine? b) How many pieces produced two machines together for five shifts?
12. Raw meat
In the school cafeteria for one lunch, they prepare 490 servings of 50 g of boiled meat. Meat loses 30% of its weight by cooking. How many kilograms of raw meat must the school canteen prepare for this lunch to cook?
13. Groups
In the 6th class there are 60 girls and 72 boys. We want to divide them into groups so that the number of girls and boys is the same. How many groups can you create? How many girls will be in the group?
14. Quotient
Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
15. 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.
16. Coach
Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach?
17. UN 1
If we add to an unknown number his quarter, we get 210. Identify unknown number.
18. Garden
The garden has the shape of a rectangle measuring 19m20cm and 21m60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent pi
19. 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?
20. Skoda cars
There were 16 passenger cars in the parking. It was the 10 blue and 10 Skoda cars. How many are blue Skoda cars in the parking?

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