# System of equations - high school - math problems

- Columns of two and three

When students in one class stand in columns of two there is none left. When he stands in columns of three, there is one student left. There are 5 more double columns than three columns. How many students are in the class? - Adam

Adam has half the money in his right pocket than in his left pocket. If he transferred 40 crowns from the left pocket to the right, he would have the same in both pockets. Calculate how many crowns does Adam have in his left pocket more than in his right? - Students

Students Aleš, Bohouš, Cyril, and Dušan were on a brigade. They divided the total revenue as follows: Aleš received two-fifths of the revenue, Bohouš received one-sixth of the revenue, Cyril received three-tenths of the revenue, and Dušan received the res - Working together

Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone? - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Contestants

The three best contestants are to divide the total prize of CZK 4,200. The second gets 20% more than the third. And the first one gets 200 CZK less than the second and the third together. How much will everyone get? - Bent scale

Monica weighed 52 kg. Sara 54 kg. Together they weighed 111 kg. They noticed that the weight on the scale was bent. How much did they really weigh? - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - Vector perpendicular

Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - The tourist

The tourist wanted to walk the route 16 km at a specific time. He, therefore, came out at the necessary constant speed. After a 4 km walk, however, he fell unplanned into the lake, where he almost drowned. It took him 20 minutes to get to the shore and re - Vector equation

Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent - Adding

Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one. - Three faces of a cuboid

The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is. - At the

At the presentation of the travelers came three times as many men than women. When eight men left with their partners, there were five times more men than women at the presentation. How many were men and women originally? - Vegetable meal

The cook was doing meal - in ratio 4: 3: 1 mix tomatoes: pepper: onion. Onions were 5 kg less than peppers. How many kgs of tomatoes did he need to prepare the meal? - Water current

John swims upstream. After a while, he passes the bottle, from that moment he floats for 20 minutes in the same direction. He then turns around and swims back, and from the first meeting with the bottle, he sails 2 kilometers before he reaches the bottle. - Guppies for sale

Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Na - TV competition

In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We - Conical bottle

When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - The percent 2

The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5% respectively. Suppose you have 3200 to invest and you want to put twice as much in the growth fund as in the money market to maximize your return. How should you i

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