# Algebra - problems - page 94

1. Rectangle - area, perimeter The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
2. Cube into cylinder If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
3. Find two Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
4. Bottle A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
5. Marriage sttus In our city, there are 3/5 of the women married to 2/3 of the men. Find what part of the population is free.
6. Inscribed rectangle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
7. Simple equation 5 Solve equation with fractions: X × 3/8 = 1/2
8. 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.
9. Beds At the summer camp, there are 41 chalets. Some rooms are 3-beds, some 4-beds. How many campers from 140 are living in 3-bed?
10. Hectares The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfor
11. Integer Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
12. Clothes Danka and Janka collect clothes. Danka had 9 more than Janka, so she gave her 7. Which now has more cloth and how many?
13. Cinema tickets Cinema sold 180 tickets this Thursday, which is 20%. Monday 14%, Tuesday 6%, Wednesday 9%, Friday 24%, Saturday 12%, and Sunday 15%. How many tickets were sold per week?
14. Simple equations Solve system of equations: 5x+3y=5 5x+7y=25
15. There There are 32 trees of three species in the orchard. 25% cherries, three eighty pears, others plums. How many plums are in the orchard?
16. Small painters There are ten pupils in the painting group. Eight pupils paint with watercolors and nine pupils with tempera colors. How many pupils paint both water and tempera colors when each pupil paints?
17. Inverted nine In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
18. Reciprocal equation 2 Solve this equation: x + 5/x - 6 = 4/11
19. A truck A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
20. A residential A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, the

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