Question

Сумма цифр двухзначного числа равна 6. Если к этому числу прибавить 18, то получится число, записанное теми же цифрами, но в обратном порядке. Найдите это число... Я знаю, ответ 24, но как его получили???

Answer 1

Xпервая цифра 
y вторая цифра
x+y=6
10x+y+18=10y+x

x+y=6
9x-9y=-18

x+y=6
x-y=-2

2x=4
x=2
y=4                            24

Answer 2

Т.к. сумма цифр =6, то это могут быть только: 1 и 5,  2 и 4,  3 и 3. Далее методом подбора получаем 24.

Answer 3

Solution to the Problem

To find the two-digit number that satisfies the given conditions, we can use algebraic equations to represent the problem and solve for the unknown number.

Let's denote the tens digit of the two-digit number as a and the units digit as b. According to the problem statement: 1. The sum of the digits is 6: a + b = 6. 2. When 18 is added to the number, the result is the number with the digits in reverse order: 10b + a + 18 = 10a + b.

Solving the Equations

We can solve these equations simultaneously to find the values of a and b.

From the first equation, we can express a in terms of b: a = 6 - b.

Substituting this value of a into the second equation, we get: 10b + (6 - b) + 18 = 10(6 - b) + b.

Solving for b: 10b + 6 - b + 18 = 60 - 10b + b, 9b + 24 = 60 - 9b, 18b = 36, b = 2.

Substituting b = 2 into the first equation, we find: a = 6 - 2, a = 4.

So, the two-digit number is 42.

Conclusion

The two-digit number that satisfies the given conditions is 42.