# Algebra - math word problems

1. Cyclist vs boat The cyclist wants to ride a short distance by boat, but when he stops at the pier, the boat does not pick up passengers yet and is preparing to leave. The cyclist decides that the boat will catch up at the next stop. The stop is 12km far along the water an
2. Apples 2 Dried apples contain 15% water. Fresh apples contain 80% water. How many kg of apples we need buy in order to get 3 kg of dried apples?
3. Diagonals of a rhombus One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
4. Alcohol mixture From 55% and 80% alcohol we have to produce 0.2 kg of 60% alcohol. How many of them do we use in solution?
5. Five members Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
6. Water wessel The vessel containing water has a weight 19 kg. After pouring half the water its weigth 11 kg. What is the weight of the empty vessel?
7. Threesome Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael.
8. Four integers Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
9. Copper parts From copper cast were made 3 parts. At first consumed one third of casting, the second 2/3 of rest and the third weighed 18 kg. What is the weight of original copper cast?
10. Internal angles Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.
11. Banknotes \$ 1390 was collected. How much was in \$20 notes and how many in \$50 notes in that order? How many solutions exists?
12. Cyclist vs car Cyclist rode out of the city at 18 km/h. 1 hour 30 minutes behind him started car and caught up with the cyclist in 50 minutes. How fast was driving the car? Where (what kilometer) from the city car overtook a cyclist?
13. Repair company The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 8 residue cars. How many total cars company repaired?
14. The plan Students have collected 48 kg of paper which is 16% of the plan. How many kg of paper still have to collect to fulfill the plan?
15. The swing To swing the two girls. Aneta weight 45 kg and Simon 35 kg weight. How far should sit Simon from the middle of swing so it is balanced, if we know that Aneta is sitting at distance 1,5m? How far are girls sitting apart?
16. Tenth member Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
17. Arm-leg Calculate the length of the base of an isosceles triangle with a circumference 224 cm if the arm length is 68 cm.
18. Equilateral triangle The equilateral triangle has a 23 cm long side. Calculate its content area.
19. Square Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg?
20. Variable Find variable P: PP plus P x P plus P = 160

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