Maths practice for 14 year olds - page 262 of 375

Number of problems found: 7493

Vacation ticket
Alena and Marta want to go on vacation together. Alena lacks CZK 300 to buy the selected ticket, and Marta has 4 times that amount left over. We know that Marta has 50% more CZK available than Alena. How much does a ticket cost?
Competitors
In the first round of the slalom, 15% of all competitors dropped out, and in the second round, another 10 competitors dropped out. In total, 40% of all competitors dropped out. What was the total number of competitors?
Number line arrangement
On the straight line representing the number axis, tie together the various points corresponding to the numbers a, 2a, 3a+1 in all possible orders. For each option, decide whether such an arrangement is possible. If yes, give a specific example; if not, e
Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm³. What is its surface in dm²?
Circumscribed by triangle
Inside the rectangle ABCD, the points E and F lie so that the line segments EA, ED, EF, FB, and FC are congruent. Side AB is 22 cm long, and the circle circumscribed by triangle AFD has a radius of 10 cm. Determine the length of side BC.
Chess reward
A reward of 1200 CZK is prepared for the 4 best champions in the chess tournament. It will be divided so that the second gets half of the first, the third half of the second's reward, and the fourth half of the third. How many CZK will each person receive
Finding x for Profit
P (x) = 15x- (5x + 10,000) specify x so that P (x) = 0
Tracksuit savings
The tracksuit became cheaper by 15% later on sale and later by 10%. How many euros did Janka save if she bought this set after the second discount and paid € 45.9?
Car acceleration
The driver of a car traveling at a given moment at a speed of 72 km/h decides to overtake a car traveling at the same speed. Therefore, during 4.0 seconds, increase the speed to 90 km/h. Calculate how big his acceleration was and what path he covered when
Mother and daughter
The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
Digit equations
The digit sum of a two-digit number is 8. If we change the order of the digits, we get a number 18 smaller than the original. Identify these numbers. We are using linear equations of two unknowns.
Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage, and the largest of the three was equal to the sum of the remaining two. The conductor sai
Big number
What is the remainder when dividing 10 by 9 to 47 - 111?
Remainder
A is an arbitrary integer that gives remainder 1 in the division with 6. B is a random integer that provides the remainder with division by two. What makes remainder in a division by three products of numbers A x B?
Inscribed circle
The circle inscribed in a triangle has a radius of 3 cm. Express the area of the triangle using a, b, and c.
Chord
It is given to a circle k(r=6 cm), and the points A and B such that |AB| = 8 cm lie on k. Calculate the distance of the center of circle S to the midpoint C of segment AB.
Iron collecting
Class 7A collected 3.2 tonnes of iron, more than class 7B. Together they collected 6.4 tonnes of iron for the secondary raw material collection. How much did each class collect?
Smallest Asymmetric Power
Find the smallest natural number k for which the number 11 on k is asymmetric. (e.g. 11² = 121)
Cake duration
Four sweethearts eat ten cakes in 30 minutes. How many minutes will 27 cakes last for nine sweets?
Adela number
Adela had two numbers written on the paper. When she added their greatest common divisor and least common multiple, she was given four different numbers less than 100. She was amazed that if she divided the largest of these four numbers by the least, she

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