Question

Старинная индийская задача: «Если задуманное число умножить на 5, из полученного произведения вычесть его треть, остаток разделить на10 и к результату прибавить последовательно ½,1/3, и ¼ первоначального числа, то получим 68. Чему равно задуманное число?»

Answer 1

The Ancient Indian Problem:

The problem states that if we multiply a certain number by 5, subtract one-third of the product, divide the remainder by 10, and then add 1/2, 1/3, and 1/4 of the original number in sequence, the result will be 68. We need to find the value of the original number.

To solve this problem, let's break it down step by step:

1. Multiply the number by 5: 5x 2. Subtract one-third of the product: 5x - (1/3)(5x) 3. Divide the remainder by 10: (5x - (1/3)(5x))/10 4. Add 1/2, 1/3, and 1/4 of the original number in sequence: (5x - (1/3)(5x))/10 + (1/2)x + (1/3)x + (1/4)x 5. The result is equal to 68: (5x - (1/3)(5x))/10 + (1/2)x + (1/3)x + (1/4)x = 68

Now, let's solve the equation to find the value of x, which represents the original number.

Solving the Equation:

To solve the equation, we can simplify the expression on the left side and then isolate the variable x.

1. Simplify the expression on the left side: - Multiply through by 60 to eliminate the fractions: 6(5x - (1/3)(5x)) + 60((1/2)x + (1/3)x + (1/4)x) = 68 * 60 - Simplify: 30x - 10x + 60x + 40x + 30x = 4080 - Combine like terms: 160x = 4080 - Divide both sides by 160: x = 4080/160 - Simplify: x = 25.5

Answer:

The original number, represented by x, is 25.5.

Please let me know if there's anything else I can help you with!