# System of equations - math word problems

1. Garage There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the gara When Ben is so many years old to Adam today, Adam will be 23 years old. When Adam was as old as Ben, Ben was two years old. How old is today Ben and Adam?
3. Wine A bottle of wine costs 21 euros; and wine is 20 times more expensive than a bottle. How much a bottle cost?
4. Three granaries Three granaries hold 7,800 metric cent (q) of grain. In the first, 70 tonnes of grain was more than the second and in the third it was 120 tonnes less than in the second. How many grain were in each granary?
5. Isosceles trapezoid Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
6. Arithmetic progression In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ?
7. Krkonose CZ Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t
8. Three shapes 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
9. Guess a fraction Tom was asked to guess a fraction. The sum of 1/2 the numerator and 1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the fraction becomes 1/3. What is the fraction that Tom was asked to guess? (Leave your answer in simplest form)
10. Trees - orchard The 3/5 trees are apple trees and 1/3 of the trees are cherries. The remaining 5 trees are pear trees. How many trees are in the orchard.
11. 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?
12. Diamond diagonals Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
13. Nice prism Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
14. Grandfather The grandfather is three years older than an grandmother. The average age of the grandmother, the grandfather and their seven grandchildren is 28 years. The grandchildren have a total of 105 years. Calculate how old is grandfather.
15. Prices prices The meter of the textille was reduced by CZK 42, so 4 meters of the new price was 20 CZK cheaper than 3 meters of the original price. What was the original and new price of the textille?
16. Two workers Two workers make 138 parts/items. The first one produces 30% more than the second. How many items will each produce?
17. Every day 7 pages Adelka reads the book every day 7 pages. When she reads one more page a day she will read it three days earlier. How long will Adelka read a book? How much does a book of pages have?
18. Linear function What is the equation of linear function passing through points: a) A (0,3), B (3,0) b) A (-2,-6), B (3,4)
19. Mr and Mrs Mr. Calda and Mrs. Cald have a total of 139 years. How many years have when we know that Mr. Calda is 9 years older than Mrs. Cald
20. Plot The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the rectan

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