# Reason - math word problems

1. Rectangles
How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm?
2. Digit sum
How many are three-digit numbers that have a digit sum of 6?
3. No smoke
Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with the cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. The regular cigarette contains 0.8 mg of nicotine. How much nicotine would a giant
4. Square into three rectangles
Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
5. Lunch
Seven classmates go every day for lunch. If they always come to the front in a different order, will be enough school year to take of all the possibilities?
6. 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: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
7. Digits
Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.
8. 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 cm2. What dimensions can this large rectangle have? Write all options. Explain your calc
9. Utopia Island
A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Ut
10. Glass with icecream
We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be?
11. 40% volume
40% volume with 104 uph (units per labor hour) 8 people working. What is the volume?
12. 3 cats
3 cats eat 3 mice in 3 days. How many mice will eat 10 cats in 10 days?
13. 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?
14. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
15. Gold inheritance
The king divided the inheritance with his three sons in the ratio of 7: 6: 4. Two of them received 286,000 gold. How much each of the sons got.
16. 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.
17. Rectangles
The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?