Algebra - problems - page 61

Trees - orchard
The 3/5 trees are apple trees and 1/3 of the trees are cherries. The remaining 5 trees are pear trees. How many trees are in the orchard.
Geometric sequence 4
It is given geometric sequence a₃ = 7 and a₁₂ = 3. Calculate s₂₃ (= sum of the first 23 members of the sequence).
Contestants
In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contestan
Population
What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
Two planes
Two planes flying from airports A and B, 420 km distant against each other. Plane from A took off 15 minutes later and flies at an average speed of 40 km/h higher than the plane from B. Determine the average speed of this two aircraft if you know that it
Cost reduction
Two MP3 players whose price was equal to originally have been discounted the first by 20%, the second by 35%. After the price reduction was the difference in their prices 750, - CZK. What was the original price of each of the two players?
Geometric sequence 5
About members of geometric sequence we know: ? ? Calculate a₁ (first member) and q (common ratio or q-coefficient)
Family parcels
In father will he divided the land so that the older son had three bigger part than younger son. Later elder son gave 2.5 ha field to younger and they had both the same. Determine the area of family parcel.
Two numbers
$fractal_6$ The sum of the two numbers is 1. Find both numbers if you know that half of the first is equal to one seventh of the second number.
Cruise liner
Cruise liner runs along the river between points A and B. The journey downstream takes 40 minutes 1 hour upriver. The flow rate of the river is 3 km/h. What is the speed of cruise liner?
Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
MO Z6-6-1
Write integers greater than 1 to the blanks in the following figure, so that each darker box was product of the numbers in the neighboring lighter boxes. What number is in the middle box?
How old
The student who asked how many years he answered: "After 10 years I will be twice as old than as I was four years ago. How old is student?
Bread
5 of the same bread has the same weight as three bread and 4 kg of fruit. What weight has one bread?
Pyramid Z8–I–6
Each brick of pyramid contains one number. Whenever possible, the number in each brick is lowest common multiple of two numbers of bricks lying directly above it. That number may be in the lowest brick? Determine all possibilities.
Unknown number 5
Daniel think an integer. When he change this number at a ratio of 2:5 he got number 2.8. Determine what number think Daniel.
Rabbits 3
Viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with Viju?
Glass
Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co
Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm^3.
Ruler
How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.

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