# Mean + system of equations - math problems

#### Number of problems found: 34

- Classs mean

Class size is 30 students, math was not worse than sign 2. Determine the number of pupils who were sign 1 if the class had a 1.4 sign average. - Flowerbed

Ondra digs the bed in 20 minutes. Cuba in 30 minutes. For how long do they dig together? - Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle? - Nuts

Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts. - Triangle midpoints

Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC. - Water current speed.

Two cities along the river are 100 km apart. The powerboat downstream runs for 4 hours, upstream for 10 hours. Determines the river's current speed. - 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? - Two pumps

Pump A takes twice as long to fill a tank than B . Together they take 2 hours to fill the tank. How long does each one take to fill the tank by itself? - Team

The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player? - Sequences AP + GP

The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members. - Two workers

Two workers work together and perform the job in 12 hours. If one has done half the work and then the second worker next half of the work it will take 25 hours. How long would it take job them separately? - Big family

A certain number of people met at the family celebration - their average age was three times the number present. Then came my grandfather, who was 75 years old and the average age was again three times the number present. How many people are celebrating r - Grandfather

The grandfather is three years older than an grandmother. The average age of the grandmother, the grandfather and their seven grandchildren is 28 years. The grandchildren have a total of 105 years. Calculate how old is grandfather. - Two valves

Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 days. How many days took to fill the pool each of the valves individually? - Certificate

There is 31 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 2. How many students have mark 1 and how many mark 2? - Work together

Michal and Dorota would do the work together in 2.25 hours. If Dorota had to do it herself, it would have taken her 6 hours longer than Michal. Determine the time that Dorota would do the work herself and the time that Michal would do it himself. - Workers

Workers A and B will done work together for 15 days. They worked together 13.5 days. Then A worker became ill and worker B finish the job alone for 7.5 days. If every worker was working alone, how many days took whole work for worker A and B? - Exam average

Average of marks that have on the certificates students of 8.A class in mathematics is exactly 2.45. If we did not add 1 and 3 of sutdents Michael and Alena, who arrived a month ago, it would average exactly 2.5. Determine how many students have class 8.A - Forth and back

Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B? - The pool

The pool contains 220 m^{3}of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B?

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