# System of equations - math word problems

1. 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.
2. Elimination method Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
3. Football season Dalibor and Adam together scored 97 goals in the season. Adam scored 9 goals more than Dalibor. How many goals scored each?
4. Nuts Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts.
5. Coins Denis and Zdeno together have 97 coins. If Denis had 4 coins less than he has now, the number of the coins would be in the ratio 14: 17. Determine the number of coins owned by Denis and Zdeno.
6. 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.
7. Spain vs USA Spain lost to the US by 4 goals. In the match total fell 10 goals. How many goals gave the Spain and how the United States?
8. 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?
9. Blackberries Daniel, Jolana and Stano collected together 34 blackberries. Daniel collected 8 blackberries more than Jolana, Jolana 4 more than Stano. Determine the number blackberries each collected .
10. Chocholate pyramid How many chocolates are in the third shelf when at the 8th shelf are 41 chocolates in any other shelf is 7 chocolates more the previous shelf.
11. 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.
12. 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.
13. Bonbons Create a mixture of 50 kg of candy on price 700Kč. Candies has prices: 820Kč, 660Kč and 580Kč. Use cross rule.
14. Jam Jar with jam weighs 800 grams. Jam weighs three times as much as the empty glass. What is the weight of jam that is in the glass?
15. The car The car has traveled the distance between A and B for four hour. If we increased the average by 17 km/h the car travel this distance an hour earlier. Determine the initial speed of the car and the distance between A and B.
16. Trapezoid trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
17. Boys and money 270 USD boys divided so that Peter got three times more than Paul and Ivan has 120 USD more than than Paul. How much each received?
18. 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?
19. 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?
20. 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?

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