# Examples for 9th grade

- A fisherman

A fisherman buys carnivores to fish. He could buy either 6 larvae and 4 worms for $ 132 or 4 larvae and 7 worms per $ 127. What is the price of larvae and worms? Argue the answer. - RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm. - Six workers

Six workers planned to repair the roof in 5 days. After two days, two workers get sick. How long will the remaining workers complete the roof at the same rate of work? - One three

We throw two dice. What is the probability that max one three falls? - Four painters

The company sent four painters to paint the school. They should be done in 12 days. After three days, one painter got ill. How long will the remaining painters paint the school? - Find the 10

Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines? - Carla

Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter’s age was twice the sum of Carla’s and Jim’s age. Find the present age of each one of them. - Height of the room

Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room? - Perimeter of RT

Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm^{2}. - Banknotes

How many different ways can the cashier payout € 310 if he uses only 50 and 20 euro banknotes? Find all solutions. - Assembly parts

Nine machines produce 1,800 parts on nine machines. How many hours will it produce 2 100 parts on seven such machines? - Seven workers

Seven workers clear the glade in 22 hours. How many workers would need to be done in 8 hours? - Concentric circles

There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area? - Sphere floating

Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. ) - Lathe

95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class? - Former price

The price of an article is cut by 10%, to restore it to the former value, by what percent the new price must be increased? - Percent change

If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent? - Curiosity factor

A blogger starts a new website, initially the number of the traffic is 293 due to their curiosity factor. The business owner estimated that the traffic will increase by 2,6% per week. What will be the number of it in week 5?. - Diamond and diagonals

A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!) - Castle model

The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm^{2}of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of wo

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