# Grade - examples - page 67

1. Florist
Florist has 84 red and 48 white roses. How many same bouquets can he make from them if he must use all roses?
2. Copiers
The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?
3. Angles and sides of the triangle
Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
4. Alloy
The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to.
5. Trousers
In the class was 12 students. Nine students wearing trousers and turtleneck eight. How many students worn trousers with a turtleneck?
Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
8. Parallelogram - side
Calculate the length of the side of a parallelogram whose area is 175 dm2 and height to that side is 24.2 dm long.
9. See harmonics
It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
10. Logarithmic equation
Solve equation: log33(3x + 21) = 0
11. Two workers
Two workers make 138 parts/items. The first one produces 30% more than the second. How many items will each produce?
12. 7 triangle
The triangle area is 26.7 cm2. Determine the side length l if appropriate height hl = 45.3 cm.
13. Arc
Convert to arc measures (radians): 924 ° Result write as a multiple of π
14. To the cinema
Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in.
15. Workhorses
A team of colleagues done the work in 20 days. After adding 2 colleagues from the beginning the work was completed in 15 days. How many members has the colleague team?
16. Ratio
Unfold number 1963 in the ratio 9:2:2.
17. Sphere area
A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
18. TV commercials
For the typical one-hour prime-time television slot, the number of minutes of commercials is 3/8 of the minutes of the actual program. Determine how many minutes of the program are shown in that one hour.
19. Fraction
Determine for what x fraction ?:
20. Hiker and cyclist
At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker?

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