# Equation - 8th grade (13y) - examples

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

1. Together
Grandfather, father, and son are carpenters. They decided to make a wardrobe. Father produces it for 12 hours, his son for 15 hours, and grandfather for 10 hours. How long will they make it together?
2. Bamboo
Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
3. In and out
The empty tank is filled in 12 minutes and empty in 16 minutes. How long does it take to fill if we forgot to close the drain? If the tank has 1000 l.
4. 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?
5. Dried fruit
The manufacturer produces a mixture of dried fruit. He purchased: 10kg pineapple for 200 Kc/kg 2kg papaya for 180 kc/kg 1kg of banana for 400 Kc/kg How many kgs of raisin for 80 Kc/kg must be put into the mix by the manufacturer so that the production pr
6. Work
The first worker would need less than 4 hours to complete the task than the other worker. In fact, both workers worked for two hours together, then the first worker did the remaining work himself. In what proportion should the remuneration of the workers b
7. Orchard
One-eighth of the trees in the fruit plant in winter froze and one-twelfth of damaged disease and pests. Healthy trees remained 152. Is it enough to supply 35 trees to restore the original number of trees in the orchard?
8. 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?
9. 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?
10. 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?
11. 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.
12. Garden
Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?
13. Pool
If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately?
14. Forestry workers
In the forest is employed 63 laborers planting trees in nurseries. For 11 hour work day would end job in 43 days. After 14 days, 22 laborers go forth. How many days is needed to complete a planting trees in nurseries by others, if they will work 15 hours
15. Bonus
Gross wage was 1762 USD including 22% bonus. How many USD were bonuses?
16. Right Δ
Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
17. Troops
Route is long 203 km and the first day first regiment went at an average speed 20 km/h and journey back 19 km/h. The second day went second regiment same route at an average speed 18 km/h there and back. Which regiment will take route longer?
18. Motion problem
From Košíc to Bratislavy go car at speed 76 km/h. From Bratislavy to Košíc go another car at speed 60 km/h. How many minutes before the meeting will be cars 22 km away?
19. Excavation
Mr. Radoslav calculated that excavation for a water connection dig for 10 days. His friend would take 7 days. Radoslav worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?
20. Logic
A man drinks a barrel of water for 31 days, woman for 58 days, for how many days they drink barrel together?

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