Examples for secondary school students - page 139 of 231

Number of problems found: 4612

Planting Ornamental Trees Ways
The gardener is to plant 6 ornamental trees. There are 8 different types of trees available. Two trees, A and B, will be planted on the left edge. How many ways can a gardener do this if all the saplings planted are to be different?
Circumference of a triangle
The circumference of the triangle is 104 cm. One side is 6 cm longer and 8 cm shorter than the third. Find the lengths of its sides.
Worker hours
One worker makes 15 parts per hour, the other 12, and the third 10. How many hours did each work when they worked together for 15 hours?
Arranging Coats Display
The arranger is to display three identical beige, two identical green, and one black coat in the shop window. How many ways can it do that?
Bottles
The must is sold in 5-liter and 2-liter bottles. Mr. Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
Equation solving
Solve the equation (y + 5 / y-3) + (y + 3 / y-5) = 3
Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the garden's width and length will increase by 3 meters, its original size will increase by 0.9
Number product increase
The product of the two numbers is 504. When one of them increases by six, the product increases to 720. It determines both factors.
Bridge cards
How many bridge hands are possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts?
Dimensions of a cylinder
We rolled a cylinder shell with a volume of 18 / π dm³ from a rectangle with an area of 6 dm². Calculate the dimensions of the rectangle.
Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in a ratio of 3:2. Volumes of a sphere and cuboid are in a ratio of 1:3. At what rate are the volumes of a cube, cuboid, and sphere?
Bags in Decreasing Rows
We will put 900 bags in nine rows, with five fewer in each subsequent one. How many are in the first place?
Evaluation of expressions
If a²-3a+1=0, find (i)a²+1/a² (ii) a³+1/a³
Expression with powers
If x-1/x=5, find the value of x⁴+1/x⁴
Speed of car
The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
Cancel fractions
Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
Permutations Equation Elements
Seven times the permutations of n elements equal one-eighth of the permutations of n + 2 elements. What is the number of elements?
Natural Numbers Less 400
How many natural numbers less than 400 can I assemble if the numbers do not repeat?
Candy and boxes
We have some candy and empty boxes. When we put ten sweets in boxes, two candies and eight empty boxes will be left. When of eight, there will be six candies and three boxes left. How many candy and empty boxes are gone when we put nine sweets into a box?
Young mathematician
One young mathematician was bored again. He found that the average age of people in the room where the seminar is held is equal to its count. Then, his 29-year-old brother entered the room. Even then, the average age of all present was the same as the cou

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