Math Problem Statement

請給我這些題目的詳答

請給我這些題目的詳答

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:

  1. Finding maximum students (a):
    • Each student can receive up to 8 bottles. Thus, the minimum number of students, aa, is 60÷8=7.560 \div 8 = 7.5, 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