Math Problem Statement
Solution
The problem from the image involves Sinta distributing chocolates to her friends, with a remaining amount each time. Let's break it down.
The information provided is as follows:
- Sinta buys a certain amount of chocolates.
- If she divides them equally among 4 friends, there are 2 chocolates left.
- If she divides them equally among 5 friends, there are 2 chocolates left.
- If she divides them equally among 8 friends, there are 6 chocolates left.
- The total number of chocolates is less than 40.
We need to find how many chocolates Sinta initially bought.
This is a case of solving for a number that satisfies all the conditions:
- The number of chocolates leaves a remainder of 2 when divided by 4 and 5.
- The number leaves a remainder of 6 when divided by 8.
- The number is less than 40.
Let's solve this step by step.
The conditions can be written as:
I'll solve this and get back to you with the exact number of chocolates Sinta bought.It seems that using a direct symbolic method for solving the modular system isn't possible in this case. However, we can use a more direct numerical approach to find the solution by checking for values of that satisfy all three modular conditions (less than 40).
Let me compute this another way.
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Math Problem Analysis
Mathematical Concepts
Modular Arithmetic
Number Theory
Formulas
x ≡ 2 (mod 4)
x ≡ 2 (mod 5)
x ≡ 6 (mod 8)
Theorems
Chinese Remainder Theorem
Suitable Grade Level
Grades 6-8
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