# System of equations - math word problems

1. Father and son
Father and son weigh together 108kg. The father weighs 2.6 times more than his son. How much does weight my father and son count?
2. AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
3. Linear system
Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2
4. The tourist
The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus gone?
5. Three brothers
The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
6. Two diggers
Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
7. Supplementary angles
One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
8. Tickets 4
Stacey is selling tickets to the school play. The tickets are \$7 for adults and \$5 for children. She sells twice as many adult tickets as children's tickets and brings in a total of \$342. How many of each kind of ticket did she sell?
9. Two resistors
Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
10. Equations - simple
Solve system of linear equations: x-2y=6 3x+2y=4
11. Barrel with water
The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
12. Integer
Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
13. Inverse matrix
Find out inverse by Gauss elimination or by reduction method. A=[2/3. 1 -3. 1/3]
14. Stamps 2
Dennis spent 34.15 on stamps. The number of .56 is 10 less than four times of stamps bought for .41. How many of each stamp did he buy?
15. Boys to girls
The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally?
16. Flowers 2
Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there?
17. Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
18. New ratio
The ratio of ducks and chicken in our yard is 2 : 3. The total number of ducks and chickens together is 30. Mother gave 3 of the chickens to our neighbor. What is the new ratio now?
19. Parking
At a building parking, 245 spaces are for cars, 56 are for vans and the rest are for buses. If 14% of all parking spaces are for buses, how many parking spaces are there in the building? How many spaces are for buses?
20. Two pumps
Pump A takes twice as long to fill a tank than B . Together they take 2 hours to fill the tank. How long does each one take to fill the tank by itself?

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