# Mean + system of equations - math problems

the arithmetic mean (simply the mean or average) is the sum of a collection of numbers divided by the count of numbers in the collection. The arithmetic mean is the most commonly used and readily understood measure of central tendency in a data set. It is a statistical characteristic of the center of a given data set.

Arithmetic mean is a quantity very sensitive to extreme values, so the median and mode are also used in practice. Mode is the most common value. The median halves the ordered file.

#### Number of problems found: 31

• 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?
• 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?
• 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?
• 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 m3 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?
• Three groups
In the company, employees are divided into three groups. In the first group, which includes 12% of the company's total number of employees, the average salary is CZK 40,000, in the second group CZK 35,000, in the third group CZK 25,000. The average salary
• Quarantine cupcakes
Mr. Honse was baking quarantine cupcakes. Mrs. Carr made twice as many as Mr. Honse. Ms. Sanchez made 12 cupcakes more than Mr. Honse. If they put all their cupcakes together (which they can’t because. .. quarantine!) they would have 108 cupcakes. How may
• Pedestrian up-down hill
Pedestrian goes for a walk first at the plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back, and goes downhill at speed 6 km/h. The total walk was 6 hours. How many kilometers went pedestrian?

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