Math Problem Statement

Augšējā plauktā ir 3 reizes vairāk grāmatu nekā apakšējā. Pēc tam, kad apakšējā plauktā ielika 16 grāmatu, bet no augšējā plaukta izņēma 20 grāmatu, abos plauktos grāmatu skaits bija vienāds. Aprēķini, cik grāmatu bija katrā plauktā sākumā!

Solution

This problem is in Latvian. Here's the mathematical question extracted and explained in English:


Problem:

  • The number of books on the upper shelf is three times more than on the lower shelf.
  • Then, 16 books are added to the lower shelf, and 20 books are taken from the upper shelf.
  • After these changes, the number of books on both shelves becomes equal.
  • Calculate the initial number of books on each shelf.

Solution:

Let:

  • xx: the number of books on the lower shelf initially.
  • 3x3x: the number of books on the upper shelf initially.

After the changes:

  • The lower shelf has x+16x + 16 books.
  • The upper shelf has 3x203x - 20 books.

From the problem, after the changes, the books on both shelves are equal: x+16=3x20x + 16 = 3x - 20

Solve for xx: x+16=3x20x + 16 = 3x - 20 16+20=3xx16 + 20 = 3x - x 36=2x36 = 2x x=18x = 18

So:

  • Initially, the lower shelf had x=18x = 18 books.
  • The upper shelf had 3x=543x = 54 books.

Final Answer:

  • Lower shelf: 18 books.
  • Upper shelf: 54 books.

Would you like a detailed step-by-step explanation or have additional questions? Here are 5 related questions for practice:

  1. What happens if instead of 16 books being added to the lower shelf, only 10 books are added?
  2. How would the calculation change if the upper shelf initially had 4 times more books than the lower shelf?
  3. What is the total number of books after the changes in the problem?
  4. Can you create a similar problem involving three shelves instead of two?
  5. How would this problem change if books were removed from both shelves?

Tip: When translating word problems into equations, focus on key quantities and their relationships.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Equation: x + 16 = 3x - 20

Theorems

Basic Algebraic Manipulation

Suitable Grade Level

Grades 7-9