# Algebra - problems

- Sand castle

Tim and Tom built a sand castle and embellished it with a flag. Half the pole with the flag plunged into the castle. The highest point of the pole was 80 cm above the ground, its lowest point 20 cm above the ground. How high was the sand castle? - The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid. - Find parameters

Find parameters of the circle in the plane - coordinates of center and radius: ? - The work

The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take? - Three people

Three people start doing a work at a same time. The first worked only 2 hours. The second ended 3 hours before the end. On an individual basis, it would take the first time to do the work 10 hours, second 12 hours and 15 hours third. How many hours did it. - Find the 9

Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3 - Profit growth

The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in the year 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods? - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - The King

The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them? - Luggage and air travel

Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lugg - MG=7x-15,

MG=7x-15, FG=33, x=? Point M is the midpoint of FG. Find unknown x. - Midpoint 6

FM=8a+1, FG=42, a=? Point M is the midpoint of FG. Find unknown a. - Midpoint 5

FM=3x-4, MG=5x-26, FG=? Point M is the midpoint of FG. Use the given information to find the missing measure or value. - Find midpoint

FM=5y+13, MG=5-3y, FG=? M is the midpoint of FG. Use the given information to find the missing measure or value. - 3rd dimension

The block has a surface of 42 dm^{2}and its dimensions are 3 dm and 2 dm. What is the third dimension? - Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand. - Lumberjacks

Fifteen lumberjacks would take 12 days to destroy the broken trees. How many days would this work require if 5 workers added to it after 4 days? - Cincinnati

A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth. - Ten cashiers

Ten cashiers are open at Tesco. Customers wait an average of 15 minutes. How many other cashiers have to open to reduce the waiting time by 4 minutes? - Coins

The boy collected coins with value 5 CZK and 2 CZK when he had 50 pieces saved 190 CZK. How many he has each type of coin?

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