# Examples for 9th grade - page 37

- Pytagoriade

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 - Two workers

Two workers make 138 parts/items. The first one produces 30% more than the second. How many items will each produce? - 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. - Arc

Convert to arc measures (radians): 924 ° Result write as a multiple of π - 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? - Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)? - 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? - 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. - Distance

Wha is the distance between the origin and the point (18; 22)? - Pot

Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm. - Scouts

Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together? - Bases

The length of the bases trapezium are in ratio 4:5. Length of midline is 15. How long are the bases of a trapezoid? - Journey

Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes? - Three-digit numbers

How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)? - Pool 2

The first supply by the pool fill for five hours and the second fill for six hours, drain should be drained for 15 hours. For how many hours the pool is full, when we open both inlet now and outlet open two hours later? - Acreage

What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ? - Sheep

Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman? - Similarity

Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity. - Hop-garden

The length of the rectangular hop garden Mr. Smith increased by 25% and its width by 30%. What is the percentage change in area of hop garden? - Word problem

395 students were on holiday in Hungary. 110 bought pizza, chips 21 pupils, 26 pupils bought soda, butter 18 pupils, 12 pupils fruits, vegetables 29 students. How much pay for all the food, if every meal cost 5.5 euros?

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