Question

Ежемесячный доход семьи складывается из зарплаты отца и зарплаты матеры. Зарплату отца увеличили на 35%, а зарплату матери – на 5%, в результате чего семейный доход увеличился на 30%. Во сколько раз зарплата отца до повышения была больше зарплаты матери?

Answer 1

З/п отца x рублей, з/п матери y руб. Семейный доход (x+y) руб.

Когда отцу увеличили з/п на 35%, он стал получать x+x*35% = x+0,35x = 1,35x руб, когда матери увеличили з/п на 5%, она стала получать y+y*5% = y+0,05y = 1,05y руб, и семуный доход составил (1,35x+1,05y). Этот доход на 30% болше первоначального, то есть

$\frac{1,35x+1,05y}{x+y}\cdot100\%-100\%=30\%\\\frac{1,35x+1,05y}{x+y}-1=0,3\\\frac{1,35x+1,05y}{x+y}=1,3\\1,35x+1,05y=1,3x+1,3y\\0,05x=0,25y\\\frac xy=\frac{0,25}{0,05}=5$

Answer 2

Calculation of Family Income Increase

To calculate the increase in family income, we need to determine the ratio of the father's salary to the mother's salary before the increase. Let's assume the father's salary before the increase is represented by x and the mother's salary before the increase is represented by y.

The father's salary was increased by 35%, which means the new salary is 135% of the original salary. Mathematically, this can be represented as:

New father's salary = 1.35x

Similarly, the mother's salary was increased by 5%, which means the new salary is 105% of the original salary. Mathematically, this can be represented as:

New mother's salary = 1.05y

The family income increased by 30%, which means the new income is 130% of the original income. Mathematically, this can be represented as:

New family income = 1.30(x + y)

Now, we can set up an equation to solve for the ratio of the father's salary to the mother's salary before the increase:

1.30(x + y) = 1.35x + 1.05y

Simplifying the equation:

1.30x + 1.30y = 1.35x + 1.05y

Rearranging the terms:

0.25x = 0.25y

Dividing both sides by 0.25:

x = y

This means that the father's salary before the increase was equal to the mother's salary before the increase. Therefore, the father's salary was not larger than the mother's salary before the increase.

Please let me know if you need any further clarification or assistance!