Math Problem Statement
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:
- : the number of books on the lower shelf initially.
- : the number of books on the upper shelf initially.
After the changes:
- The lower shelf has books.
- The upper shelf has books.
From the problem, after the changes, the books on both shelves are equal:
Solve for :
So:
- Initially, the lower shelf had books.
- The upper shelf had 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:
- What happens if instead of 16 books being added to the lower shelf, only 10 books are added?
- How would the calculation change if the upper shelf initially had 4 times more books than the lower shelf?
- What is the total number of books after the changes in the problem?
- Can you create a similar problem involving three shelves instead of two?
- 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
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