# Algebra - problems - page 38

1. Fewer than 500 sheep,
There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain. But they can stand in the seventh order. How many are sheep?
2. 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?
3. Trapezoid 15
Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
4. Floor
Rectangular floor of living room has a length 5.4 meters and a circumference 17.2 meters. What is its width?
5. The field
The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
6. Rings - intersect
There are 15 pupils on the sporting ring. 10 pupils go to football, 8 pupils go to floorball. How many pupils go to both rings at the same time?
7. Unknown number
Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
8. Rhombus
One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
9. Arithmetic average
The arithmetic mean of the five numbers is exactly 8. The sum of these four numbers is 30. What is the fifth number?
10. The city
In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
11. Welders
Welder do the job for six hours, the second one for 8 hours. How long do the job third welder if all together can do job in 2 hours?
12. Pagans
Elena cut out same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagans occupied 28.26 cm2 of the bottom of the sheet.
13. Mr. John
Mr. John wants to buy winter apples Spartan. There are two ways to buy: 1) buy apples at the marketplace, where 1 kg costs 15 CZK. 2) Bring the car to the agricultural farm, where the apples are sold after 9 CZK per kilogram. However, he must pay CZK 150.
14. The creek
Workers cleaned the creek within 3 days. The first day cleanse one-fifth the length of the creek, the next day 40% of the length of the stream and the third day 8 km length of the creek. How long is a creek?
15. Tubes
Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes?
16. Digits of age
The product of the digits of Andrew age as 6 years ago and not equal to 0. Andrew age is also the smallest possible age with this two conditions. After how many years will be the product of the digits of Andrew age again the same as today?
17. James
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?
18. Three Titanics
Three steamers sailed from the same port on the same day. The first came back on the third day, fourth 4th day and the third returned sixth day. How many days after leaving the steamers met again in the harbor?
19. Purchase
Three buyers pay € 468. The first paid 3-times more than second, third half over second. How many euros paid each of them?
20. Equation
How many real roots has equation ? ?

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