Algebra - math word problems

Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
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 the 9
Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
The sponsor
The school received money from the sponsor. She used one-third to buy computers, half of the rest to adjust the gym. It still has 4000 euros left. How many euros did the sponsor donate to the school?
Small painters
There are ten pupils in the painting group. Eight pupils paint with watercolors and nine pupils with tempera colors. How many pupils paint both water and tempera colors when each pupil paints?
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
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?
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?
Spherical cap 4
What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
Four workers
Four workers will lay the floor of the gym in six hours. After an hour of working together, one of the workers left to the doctor. How long before the remaining three workers finish their work?
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.
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.
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.
3rd dimension
The block has a surface of 42 dm² and its dimensions are 3 dm and 2 dm. What is the third dimension?
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 lug
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?

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