Question

Если к некоторому двухзначному приписать на конце ноль, то это число увеличится на 234. Найти это двухзначное число. Заранее спасибо.)

Answer 1

Пусть х будет задуманное число,если к нему приписать нолик,это будет все равно,что умножить на 10,составим уравнение :

10х = 234 + х

10х - х = 234

9х = 234

х = 26

Answer 2

Problem Analysis

We are given that if we append a zero at the end of a two-digit number, the resulting number increases by 234. We need to find this two-digit number.

Solution

Let's assume the two-digit number is represented by 'AB', where A is the tens digit and B is the units digit. When we append a zero at the end, the resulting number becomes 'AB0'. According to the given information, this number increases by 234. Mathematically, we can represent this as:

AB0 = AB + 234

To solve this equation, we can subtract AB from both sides:

AB0 - AB = 234

The left side of the equation can be simplified by factoring out AB:

A * 10 + B * 1 - A * 1 - B * 1 = 234

Simplifying further:

9A = 233

Dividing both sides by 9:

A = 233 / 9

Calculating the value of A:

A = 25.888...

Since A represents the tens digit, it must be a whole number. Therefore, we can round down A to the nearest whole number:

A = 25

Now, we can substitute the value of A back into the equation to find B:

AB0 = AB + 234

250 = 25B + 234

Subtracting 234 from both sides:

16 = 25B

Dividing both sides by 25:

B = 16 / 25

Calculating the value of B:

B = 0.64...

Since B represents the units digit, it must be a whole number. Therefore, we can round B to the nearest whole number:

B = 1

So, the two-digit number that satisfies the given condition is 25.

Answer

The two-digit number that, when a zero is appended at the end, increases by 234 is 25.