# Algebra - math word problems

1. 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.
2. A rectangular patio A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
3. Lateral surface area The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
4. Two cubes The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
5. Rectangular trapezoid In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
6. A fisherman A fisherman buys carnivores to fish. He could buy either 6 larvae and 4 worms for \$ 132 or 4 larvae and 7 worms per \$ 127. What is the price of larvae and worms? Argue the answer.
7. A photograph A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.
8. Here is Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.
9. Rectangular garden 2 A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
10. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
11. 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?
12. Expression If A=2 B=3 evaluate expression A(B+A) and multiply it by A
13. Four painters The company sent four painters to paint the school. They should be done in 12 days. After three days, one painter got ill. How long will the remaining painters paint the school?
14. Carla Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter’s age was twice the sum of Carla’s and Jim’s age. Find the present age of each one of them.
15. Perimeter of RT Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
16. Banknotes How many different ways can the cashier payout € 310 if he uses only 50 and 20 euro banknotes? Find all solutions.
17. Concentric circles There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
18. Bonuses Five employees of the company were paid bonuses so that each successor received a 550 USD less than the previous employee. How much did everyone get, if a total of USD 11,000 has paid?
19. Number of songs Write an expression for the number of songs they need for this show. Evan and Peter have a radio show that has 2 parts. They need 4 fewer than 11 songs in the first part. In the second part, they need 5 fewer than 3 times the number of songs in the first
20. Former price The price of an article is cut by 10%, to restore it to the former value, by what percent the new price must be increased?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...