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.
Motion Problems Solving Word Problems "From the End" / Working Backwards-
School Supplies
An eraser and two pencils together cost 19 lira, a pencil and two notebooks together cost 23 lira, a notebook and two
erasers together cost 18 lira. How much do an eraser, a pencil, and a notebook cost together?Sources: -
Puzzle
You have a puzzle where each piece looks like this:
The following shape is made up of 12 pieces. What is its perimeter?
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Sum of Products of Digits
Let `P(n)` denote the product of the digits of the number `n`. For example, `P(1948) = 1 * 9 * 4 * 8 = 288`.
A.
Calculate `P(1) + P(2) + P(3) + ... + P(2016)`
B.
Find the maximum value of `{P(n)} /n`, where `2016 <= n <= 5777`.
(Solution format: "x, y/z" where y/z is an unreduced fraction. For example "10000, 35/100")
Sources:Topics:Arithmetic Algebra -> Word Problems Combinatorics -> Number Tables Number Theory -> Division- Gillis Mathematical Olympiad, 2016-2017 Question 2
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Candies
In a class, there are a number of students and each has a number of candies:
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There are exactly 10 children with at least one candy,
Exactly 8 children with at least two candies,
Exactly 6 children with at least 3,
Exactly 4 children with at least 4,
And exactly 2 children with 5 candies.
It is known that no one has more than 5 candies. How many candies are there in the class? -
Doughnuts
Ayala, Benny, Gili, Danny, and Hadas received a package of doughnuts containing
- 10 doughnuts with dulce de leche
- 8 doughnuts with peanut butter
- 9 doughnuts with chocolate
- 11 with strawberry jam
Each of them has their favorite type of doughnut.
- Ayala ate 5 doughnuts of her favorite type
- Benny ate 6 doughnuts of his favorite type
- Gili ate 7 doughnuts of her favorite type
- Danny ate 8 doughnuts of his favorite type
- Hadas ate 9 doughnuts of her favorite type
After that, they were left with 3 doughnuts of different types. What is each of their favorite type of doughnut?
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Sum of Squares
Given a rectangle with an area of 13 and a perimeter of 20. On two adjacent sides of the rectangle, two squares are constructed, as shown in the figure. Find the sum of the areas of the squares.
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Zionism Street
On Zionism Street live Benjamin, Chaim, Judah, and Max. Benjamin left his house, walked 169 meters, and arrived at Chaim's house.
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After a short rest, he walked 196 meters and arrived at Judah's house. Then he walked 171 meters and arrived at Max's house.
Finally, after walking another 144 meters, he returned to his house. What is the distance from Benjamin's house to Judah's house? -
The Bakery
In the morning, a bakery's storage room contained 135 kilograms of flour and 92 kilograms of sugar.
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To bake one cake, the baker uses one kilogram of flour and one kilogram of sugar.
At the end of the workday, the amount of flour remaining for the baker was twice as large as the amount of sugar remaining.
How many cakes did the baker make during the workday? -
We went on a trip
Grade 4, consisting of 32 students, went on a trip. The students had to bring hats, sunglasses, and water bottles.
No child forgot all of these things, but:- Among the students who brought hats, 9 forgot sunglasses,
- Among the students who brought sunglasses, 7 forgot water bottles,
- And among the students who brought water bottles, 10 forgot sunglasses.
How many students in the class brought everything needed for the trip?
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The Elevator
Avi works in a multi-story building, on the top floor. His friends Benny and Gil also work in the same building. Every day, in the morning and evening, Avi goes to greet them.
In the morning Avi enters the building,- goes up 21 floors in the elevator to Benny's office,
- walks down to Gil's office,
- goes up 17 floors in the elevator to his office.
After work,
- Avi goes down 9 floors in the elevator to Benny's office,
- walks down to Gil's office,
- goes down 13 floors in the elevator and exits the building.
How many floors are in the building? (Reminder - the ground floor is also a floor)
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