Question

Зарплату учителя в начале года повысили на х%. Затем новую зарплату через месяц повысили на 2%. В результате двух повышений зарплата увеличилась в 1,224 раза. На сколько процентов зарплата была повышена в первый раз?

Answer 1

.................................................

Answer 2

(1+x/100)*1.02=1,224
1+х/100=1.2
х/100=0.2
х=20%

Answer 3

Calculating the Percentage Increase in Salary

To calculate the percentage increase in salary for the first raise, we can use the given information that the salary was first increased by x% and then increased by 2%. The resulting increase in salary was 1.224 times the original salary.

Let's denote the original salary as S. After the first increase of x%, the salary becomes S * (1 + x/100). Then, after the second increase of 2%, the salary becomes S * (1 + x/100) * (1 + 2/100).

Given that the resulting salary increase is 1.224 times the original salary, we can set up the equation:

S * (1 + x/100) * (1 + 2/100) = 1.224 * S

Solving for x will give us the percentage increase in the first raise.

Calculation

Let's solve the equation to find the value of x:

Solving the equation: S * (1 + x/100) * (1 + 2/100) = 1.224 * S

We can simplify the equation to: (1 + x/100) * (1 + 2/100) = 1.224

Expanding and simplifying: 1 + x/100 + 2/100 + 2x/10000 = 1.224 1 + x/100 + 0.02 + 2x/10000 = 1.224 x/100 + 0.02 + 2x/10000 = 0.224 100x + 2 + 2x = 22.4 102x = 20.4 x = 20.4 / 102 x ≈ 0.2

Answer

The percentage increase in salary for the first raise was approximately 0.2%.