Math Problem Statement
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Solution
Here are the solutions for questions 8, 9, and 10 on your image:
Question 8
The problem states: A teacher is distributing 60 bottles of mineral water and 100 bread rolls evenly among students. Each student receives at most 8 bottles of water and at most 4 rolls. If the maximum number of students is a and the minimum is b, what is a - b?
Solution:
- Finding maximum students (a):
- Each student can receive up to 8 bottles. Thus, the minimum number of students, , is , rounded down to 7 (but with the constraint, it’s possible to make it 15).
- Similarly,
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Math Problem Analysis
Mathematical Concepts
Division
Greatest Common Divisor (GCD)
Modular Arithmetic
Inequalities
Formulas
Division formula: Total items ÷ Items per person = Number of people
Greatest common divisor condition: gcd(a, b) = 6
Modulo condition: x % n = remainder
Theorems
Greatest Common Divisor
Properties of Modulo Operations
Suitable Grade Level
Grades 7-9
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