Algebra, Word Problems

Word problems present mathematical challenges in a narrative or real-world context. Solving them requires translating the text into mathematical equations or expressions and then applying appropriate mathematical techniques. These can span arithmetic, algebra, geometry, etc.

• Question

  `10` identical books cost more than `11` dollars, and `9` books of the same type cost less than `10` dollars. How much does one book cost?

  Topics:

  Algebra -> Inequalities Algebra -> Word Problems Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Camels and Horses

  In a herd, there are dromedary camels (one-humped), Bactrian camels (two-humped), and horses. It is known that the total number of humps in this herd is `200`. In addition, the number of horses is equal to the number of Bactrian camels. How many animals are there in the herd in total?

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic

• The Clubs

  In the grade, there are `70` children. Of these, `27` go to theater club, `32` sing in the choir, and `22` do Judo. In the theater club, there are `10` children from the choir, in the choir there are `6` children from Judo, and in Judo there are `8` children who also study theater. Three children also go to theater club, Judo, and sing in the choir. How many children from the grade do not participate in any of these three clubs?

  Topics:

  Arithmetic Combinatorics Algebra -> Word Problems Set Theory

• Watering Potted Plants

  Hannah and Rachel watered potted plants at home. It is known that each of them watered exactly half the number of potted plants in the house, and it is also known that three potted plants were accidentally watered twice. How many potted plants remain to be watered?

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Set Theory

• Question

  This year, Yossi participated in the Mathematics Olympiad for the first time. Before the Olympiad, a survey was conducted in which each participant was asked what place they thought they would achieve. Yossi answered that he would probably be in last place. After the competition itself, it turned out that every participant, except for Yossi, achieved a worse place than they answered in the survey. What place did Yossi take in the Olympiad?

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic

• Question

  A two-digit number is written on the board. Avi claims that the units digit of the number is twice the tens digit. Beni claims that the number is divisible by `9`. Gal claims that the number is divisible by `4`. Dani claims that the number is divisible by `27`. It is known that one of them is wrong, and the rest are correct. What number is written on the board?

  Topics:

  Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 2, 4, and 8 Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9 Algebra -> Word Problems Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Cherries and Blueberries

  `175` kg of cherries cost more than `125` kg of blueberries, but less than `126` kg of blueberries. In addition, it is known that a kilogram of cherries costs a whole number of shekels, and a kilogram of blueberries also costs a whole number of shekels.

  Prove that `80` shekels is not enough to buy one kilogram of blueberries and three kilograms of cherries.

  S. Fomin

  Topics:

  Number Theory Arithmetic Algebra -> Inequalities Algebra -> Word Problems
  Sources:
  • Tournament of Towns, 1983-1984, Fall, Practice Version, Grades 9-10 Question 1 Points 3

• Question

  In a room, there are round chairs with `3` legs and square chairs with `4` legs, totaling `8` chairs. How many of them are square chairs, if the total number of legs in the room is `27`?

  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question

  In Ella's building, there are three entrances and `13` floors (from `0` to `12`, and the apartments are on every floor except the ground floor). In each entrance, on each floor, there are five apartments. Ella lives in apartment number `73`. In which entrance and on which floor does she live?

  Topics:

  Algebra -> Word Problems Number Theory -> Division Arithmetic -> Division with Remainder

• Question

  Avi invited guests. They know he lives in apartment `333`, in entrance number `10`, but they don't know which floor. There are `9` floors in the building, and it is known that there are an equal number of apartments on each floor. The guests want to use the elevator. Can they calculate in advance which floor they need to press in the elevator?

  Topics:

  Algebra -> Inequalities Algebra -> Word Problems Arithmetic -> Division with Remainder