# System of equations - examples - page 20

1. Euros Peter, Jane and Thomas have together € 550. Tomas has 20 euros more than Jane, Peter € 150 less than Thomas. Determine how much has each of them.
2. 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?
3. Water wessel The vessel containing water has a weight 19 kg. After pouring half the water its weigth 11 kg. What is the weight of the empty vessel?
4. 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?
5. Banknotes \$ 1390 was collected. How much was in \$20 notes and how many in \$50 notes in that order? How many solutions exists?
6. Threesome Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael.
7. Four integers Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
8. Football match 4 In a football match with the Italy lost 3 goals with Germans. Totally fell 5 goals in the match. Determine the number of goals of Italy and Germany.
9. 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.
10. Weights Marry and John together weighing 49 kg. Their weights are in ratio 1:6. Determine their weights.
11. Electricity consumption cost Last year Karol family reduced its electricity consumption by 31% compared to the previous year and paid CZK 2883 less. How many CZK is electricity last year and how many two year ago?
12. Bag Nelly found interesting point. An empty bag weighs 4 kg less than full. And empty bag is 5 times easier than full. How many kg weigh things in this bag?
13. Difference of two number The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers.
14. Friends James and Jaroslav are friends. Together they had 48 toy cars. But if John took 8 cars from Jaroslav, Jaroslav will be have 1.5 times more toy cars than James. How many toy cars had Jaroslav and James?
15. 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.
16. Parallelogram Side a of parallelogram is twice longer than side b. Its circumference is 78 dm. Calculate the length of the sides of a parallelogram.
17. Ball game Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
18. Rectangle Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width.
19. 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.
20. Land areas Two land areas is 244 m2. The first parcel is 40 m2 less than twice of the second one. What have acreage of each parcel?

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