Math Problem Statement

Sinta membeli sekantung cokelat. Jika ia membagi cokelat tersebut kepada 4 temannya sama banyak, ada 2 cokelat tersisa di kantong. Jika ia membagi cokelat tersebut kepada 5 temannya sama banyak, tidak ada cokelat yang tersisa di kantong. Jika ia membagi cokelat tersebut kepada 8 temannya sama banyak, tersisa 6 cokelat di kantong. Diketahui banyak cokelat di kantong tidak lebih dari 40 bungkus. Berapa banyak cokelat yang dibeli Sinta?

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:

  1. Sinta buys a certain amount of chocolates.
  2. If she divides them equally among 4 friends, there are 2 chocolates left.
  3. If she divides them equally among 5 friends, there are 2 chocolates left.
  4. If she divides them equally among 8 friends, there are 6 chocolates left.
  5. 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 xx of chocolates leaves a remainder of 2 when divided by 4 and 5.
  • The number xx leaves a remainder of 6 when divided by 8.
  • The number xx is less than 40.

Let's solve this step by step.

The conditions can be written as:

  1. x2(mod4)x \equiv 2 \pmod{4}
  2. x2(mod5)x \equiv 2 \pmod{5}
  3. x6(mod8)x \equiv 6 \pmod{8}

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 xx that satisfy all three modular conditions (less than 40).

Let me compute this another way.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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