Question

Помогите решить задачу. если имеющиеся карандаши разложить в коробки по 8 штук в каждую, то остается 5 лишних карандашей. если их разложить в коробки по 6 штук в каждую, тоже останется 5 лишних карандашей. сколько имеется карандашей если их больше 50 но, меньше 100?

Answer 1

Число делится на 8,с остатком 5
Число делится 6,с остатком 5
Следовательно находим число ,делящееся на 8 и на 6
6*8=48
48+5(остаток)=53

Answer 2

Problem Analysis

We are given that if we distribute the available pencils into boxes of 8, there will be 5 extra pencils left. Similarly, if we distribute them into boxes of 6, there will also be 5 extra pencils left. We need to determine the number of pencils available, which is greater than 50 but less than 100.

Solution

Let's assume the number of pencils available is x.

According to the problem, if we distribute the pencils into boxes of 8, there will be 5 extra pencils left. This can be represented by the equation:

x mod 8 = 5 Similarly, if we distribute the pencils into boxes of 6, there will also be 5 extra pencils left. This can be represented by the equation:

x mod 6 = 5 We can solve these equations simultaneously to find the value of x.

Solving the Equations

To solve the equations, we can start by finding the common multiples of 8 and 6 that are greater than 50 but less than 100.

The common multiples of 8 and 6 are: 24, 48, 72, 96.

Checking these multiples against the equations, we find that only 96 satisfies both equations:

96 mod 8 = 0 96 mod 6 = 0 Therefore, the number of pencils available is 96.

Answer

The number of pencils available is 96.

Explanation

If we distribute the 96 pencils into boxes of 8, there will be 5 extra pencils left:

96 mod 8 = 0 (no remainder) If we distribute the 96 pencils into boxes of 6, there will also be 5 extra pencils left:

96 mod 6 = 0 (no remainder) Therefore, the number of pencils available is 96, which satisfies both conditions given in the problem.

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