# Algebra - math word problems

- Wire fence

The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure? - The half life

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives? - Half of halves

Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part? - Interior angles

Calculate the interior angles of a triangle that are in the ratio 2: 3: 4. - The farmer

The farmer calculated that the supply of fodder for his 20 cows was enough for 60 days. He decided to sell 2 cows and a third of the feed. How long will the feed for the rest of the peasant's herd last? - Probability

How probable is a randomly selected three-digit number divisible by five or seven? - The coal

The coal stock would be enough to heat a larger room for 12 weeks, a smaller one for 18 weeks. It was heated for four weeks in both rooms, then only in a smaller one. How long was the coal stock enough? - The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm^{2}. Calculate the length of the leg b and the median t2 to side b. - Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord? - The four

The four pirates divided 65 coins to each other. They were sorted by age, the youngest receiving the least number of coins, each half more than the previous one. How many coins did the oldest pirate receive? - In a

In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides. - Digging

The first worker would dig a trench in 6 hours. For the second, the same work would take 4 hours. How long did it take for the trench to be dug if they worked together? - Closed circuit

In a closed circuit, there is a voltage source with U1 = 12 V and with an internal resistance R1 = 0.2 Ω. The external resistance is R2 = 19.8 Ω. Determine the electric current and terminal voltage. - Seven

Seven dwarfs will cut 420 stumps in 15 hours. After five hours, the two dwarves disappear discreetly. How many hours will the remaining dwarves complete the task? - Students

Students Aleš, Bohouš, Cyril, and Dušan were on a brigade. They divided the total revenue as follows: Aleš received two-fifths of the revenue, Bohouš received one-sixth of the revenue, Cyril received three-tenths of the revenue, and Dušan received the res - Job applicants

Job applicants: three-fourths of applicants had experience for a position. The number that did not have prior experience was 36. How many people applied for the job? - Library

New books were purchased for the library. Five-eighths were professional books, one-fifth were encyclopedias, and 231 books were dictionaries. How many professional books were there? - The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid. - What is bigger?

Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm? - Double price reduction

The price of TV has been reduced twice. First by 15% and later by another 10% of the reduced price. After this double price reduction, the TV was sold for 8,874 crowns. What was the original price of the TV?

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