System of equations - examples - page 12
- The farmer
The farmer harvested 840 tons of grain in 2006, which was 44% less than in 2005, and one-fifth more than in 2004. How many tons of grain harvested in years 2005 and 2004?
- Passenger car and truck
From Kutna Hora left at 11:00 clock a truck at 60 km/h. At 12:30 behind him started passenger car at average speed 80 km/h. At what time and how far from Kutna Hora overtake a passenger car truck?
- Two pipes
One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
- Crown coins
Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?
In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
- Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
- Cars speeds
Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes?
- Three workers
Three workers were rewarded CZK 9200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received?
Weight of cargo car is 761 kg. Weight of car is 23% of the total weight of car+cargo. What is the weight of the cargo load?
When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet?
- Ratio of two unknown numbers
Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
- Rectangular field
One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m2 . Determine dimencions of the field.
- Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
- Have solution
The sum of four consecutive even numbers is 96. Determine these numbers.
- The city
In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether?
- Diamond diagonals
Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
Three buyers pay € 468. The first paid 3-times more than second, third half over second. How many euros paid each of them?
- Null points
Calculate the roots of the equation: ?
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