Question

Составьте уравнение по условию задачи и решите его: Марат задумал число. Из задуманного числа он отнял 16, затем разность умножил на 11, и получилось число 88. Какое число задумал ученик?

Answer 1

Problem Analysis

To solve this problem, we need to set up an equation based on the given conditions and then solve for the unknown number. Let's break down the problem step by step:

1. Marat thought of a number. 2. He subtracted 16 from the number. 3. He multiplied the difference by 11. 4. The result of the multiplication is 88.

We need to find the number that Marat initially thought of.

Setting up the Equation

Let's assume the unknown number that Marat thought of is represented by the variable 'x'. We can set up the equation based on the given conditions:

(x - 16) * 11 = 88

Solving the Equation

To solve the equation, we need to isolate the variable 'x'. Let's simplify the equation step by step:

1. Distribute the 11 to the terms inside the parentheses:

11x - 176 = 88

2. Move the constant term (-176) to the other side of the equation by adding 176 to both sides:

11x = 88 + 176 11x = 264

3. Divide both sides of the equation by 11 to solve for 'x':

x = 264 / 11 x = 24

Answer

The number that Marat initially thought of is 24.

Verification

To verify our answer, let's substitute the value of 'x' back into the original equation and check if it satisfies the given conditions:

(24 - 16) * 11 = 88 8 * 11 = 88 88 = 88

The equation is satisfied, which confirms that our answer is correct.

[SOURCE 1]