# System of equations - math word problems

1. Equilateral triangle A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
2. Father and son When I was 11, my father was 35 years old. Today, my father has three times more years than me. How old is she?
3. The train The train passed the observer in the 20s and passed through a 1500m tunnel in 2 minutes. Calculate the speed (km/h) and train length.
4. Inscribed circle Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
5. Three workshops There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
6. Mother and son Mother is four times older than her son. In 16 years, the son will be two times younger than his mother. How many years are mother and son?
7. Tea mixture Of the two sort of tea at a price of 180 CZK/kg and 240 CZK/kg we make a mixture 12 kg that should be prepared at a price of 200 CZK / kg. How many kilos of each sort of tea will we need to be mixed?
8. Tractors Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately?
9. Grandfather and grandmother The old mother is 5 years younger than the old father. Together they are 153 years old. How many years has each of them?
10. Two trains There were 159 freight wagons on the railway station creating 2 trains. One had 15 more wagons than the other. How many wagons did each train have?
11. Digit sum The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
12. Birthday Mother bought 21 desserts on the occasion of Mirka's birthday one tips was 9 CZK and the kremlin cost 12 CZK. For all desserts, she paid 213 CZK. How many kremlins and how many tips mums did buy?
13. Highway tunnel The highway tunnel was built from two ends in the north-south direction. The average daily performance of the "northern party" rasters was higher than the average daily power of the "southern party" of the rasters. After 55 business days, both parties met.
14. Two unknown numbers One number is 2 less than a second number. Twice the second number is 14 less than 5 times the first. Find the two numbers.
15. Two workers Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself?
16. T-shirts and hat 5 t-shirts and a hat cost £62.00 2 t-shirts and a hat cost £29.00 How much does a t-shirt cost ? How much does a hat cost ?
17. Substitution solve equations by substitution: x+y= 11 y=5x-25
18. Unknown numbers The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
19. Simple equations Solve system of equations: 5x+3y=5 5x+7y=25
20. Mother and daughter The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?

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