# Algebra - problems - page 99

1. 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 ?
2. Coins The boy collected coins with value 5 CZK and 2 CZK when he had 50 pieces saved 190 CZK. How many he has each type of coin?
3. Isosceles triangle In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
4. Center of line segment Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
5. Three friends Cuba, Matthew and their friend Adam found a brigade during their weekend weekends because they wanted to make a joint trip to the Alps that they planned for the spring break. Cuba enjoyed the skiing trip very much, so he was not lazy to get up and went t
6. Sum of four numbers The sum of four consecutive natural numbers is 114. Find them.
7. Tickets 1260 tickets sold. On the first day, 80% was sold on the second day was sold. How many tickets were sold first and how much the next day?
8. Coordinates of midpoint If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
9. Ditch Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth.
10. The garden The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €?
11. Drying herbs Herbs lose 75% weight By drying. How many fresh herbs do you have to collect if you want to make 1.5 kg of dried herbs?
12. Distance problem 2 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
13. Solve 2 Solve integer equation: a +b+c =30 a, b, c = can be odd natural number from this set (1,3,5,7,9,11,13,15)
14. Hotel rooms In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?
15. Simple sequence Continue with this series of numbers: 1792,448, 112, _, _
16. Symmetry by plane Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0
17. Find the 9 Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
18. Peter and Paul Peter and Paul together have 26 years. Four years ago, Paul was twice older than Peter. How much is Paul and how much Peter?
19. Bucket The bucket half filled with water weighs 5.55 kg, the full bucket weighs 9.85 kg. How much does the bucket weigh?
20. Banknotes How many different ways can the cashier payout € 310 if he uses only 50 and 20 euro banknotes? Find all solutions.

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