# Reason - math word problems - page 31

- Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Thales

Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole. - Dice

We throw five times the dice. What is the probability that six fits exactly twice? - Three friends

Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together. - Cents no more

Janko bought pencils for 35 cents each. Neither he nor the salesperson had small coins just a whole € 1 coin. At least how many pencils had to buy to pay for the whole euros? - Book reading

If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book? - Basket of fruit

In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which - Repair pipe

20 workers had to repair broken pipes in 30 days. After fourteen days, four laborers joined them. How long did the pipe repair work last? - Apples

School kitchen bought 36kg apples for 12 kc/kg. How many kilograms of apples 1/4 cheaper can they buy for the same money? - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Tractors

Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately? - Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? - The work

The work was to be done by 150 workers. At the beginning of their work, their number reduced by 40, which increased the time of work by 5 and 1/3 of the schedule. How long did work take? - ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Class alphabet

All 29 pupils in the class are written in a class by alphabet. The number of pupils enrolled before Paul is three times higher than the number of pupils behind him. Calculate how many pupils are enrolled after Paul. - Endless lego set

The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They - Candy and boxes

We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of. - Supermarket 2

A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution. - Two rectangles

I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm^{2}. What dimensions can this large rectangle have? Write all options. Explain your calcu

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