# System of equations - examples - page 21

1. Money Peter has 2x more money than Michael. But if Peter gave Michael € 16 Michael would have 3.5 times more money than Peter. Determine how much money was originally Peter and how much Michael.
2. Body diagonal The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
3. Baskets of apples Grandfather gathered apples into baskets. He filled one large and three small baskets. Small baskets are identical and each can hold 3 kg of apples less than in a large basket. In small baskets together 3 kg of apples over a large basket. How many kilogram
4. 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.
5. Isosceles trapezoid Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
6. Price saleoff Shoes standing y euros. At first they were discounted by 12% and then 50% of the new amount. After this double cheapening the cost was exactly 22 euros. Determine the original price of shoes.
7. 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
8. Linear system Solve this linear system (two linear equations with two unknowns): x+y =36 19x+22y=720
9. Unknown amount of money Damian and Denis split an unknown amount in the ratio of 5:4 . Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money got Damian and how Denis.
10. Comparing salaries Spouses compared salaries. Mrs. Janka found that a 20% higher salary than Mr Jaroslav. Together earned € 1,430. How much they earn each of them?
11. 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?
12. Blueberries Miko and Anton have a total of 1,580 blueberries. Miko and Anton have them in the ratio 2: 3. Determine how much each of them has.
13. 3 masons 3 masons received 7,700 CZK. The second half received 1/2 more than the first and third twice more than the second mason. How much they each got crowns?
14. AP - basics Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
15. Two sisters Two sisters together have 54 CDs. 6/8 CDs has younger sister and is equal to 3/5 of CDs older sisters. How many CDs has each of the sisters?
16. Wine A bottle of wine costs 21 euros; and wine is 20 times more expensive than a bottle. How much a bottle cost?
17. Boxes 200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row?
18. Football season Dalibor and Adam together scored 97 goals in the season. Adam scored 9 goals more than Dalibor. How many goals scored each?
19. Benches The park has 64 benches. Occupied are by 18 more than empty. How many benches are occupied and empty ?
20. Warehouses In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?

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