# Algebra - problems - page 98

1. Sum of two primes Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
2. Equation 15 Solve equation with variables on both sides:
3. Three numbers We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
4. A man 2 A man divides \$10,000 into two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.
5. Luggage and air travel Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lugg
6. Two thirds Find two-thirds of the number equal to two-thirds of 99
7. Three brothers The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
8. Six workers Six workers planned to repair the roof in 5 days. After two days, two workers get sick. How long will the remaining workers complete the roof at the same rate of work?
9. Employees There are 1116 people working in three factory halls. In the first one, there are 18% more than the third, and 60 persons more than the second. How many employees work in individual halls?
10. Bricklayer How much do we pay for a bricklayer laying a pavement in a square room with a diagonal of 8 m, if 1 sqm with work will cost for CZK 420?
11. Negative in equation 2x + 3 + 7x = – 24, what is the value of x?
12. Circle annulus There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
13. Brick weight Half the weight of a brick plus 20 pounds is equal to 1/3 the weight of the brick plus 30 pounds. How much does the brick weigh?
14. Girls The children's competition was attended by 63 girls, which is 30% of all children's participants. How many children attended this competition?
15. The sum 2 The sum of five consecutive even integers is 150. Find the largest of the five integers. A.28 B.30 C.34 D.54 Show your solution and explain your answer.
16. Area to volume If the surface area of a cube is 486, find its volume.
17. Reminder and quotient There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S, D:S are with the remainder of 1,
18. A cylindrical tank A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
19. Ratio of sides Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
20. Test scores Jo's test scores on the first four 100 point exams are as follows: 96,90,76, and 88. If all exams are worth the same percent, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)?

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