Question

Семья состоит из мужа, жены и их дочери-студентки. Если бы зарплата мужа увеличилась вдвое, общий доход семьи вырос бы на 62 %. Если бы стипендия дочери уменьшилась на треть, общий доход семьи сократился бы на 3 %. Сколько процентов от общего дохода семьи составляет зарплата жены?

Answer 1

Пошаговое объяснение:

Пусть зарплата мужа равна х, зарплата жены равна у, зарплата дочери-студентки равна z, а общий доход семьи - 100%.     ⇒

$\left\{\begin{array}{ccc}x+y+z=100\%\\2x+y+z=162\% \\x+y+\frac{z}{3} =97\% \ |*3\end{array}\right.\ \ \ \ \left\{\begin{array}{ccc}x+y+z=100\%\\2x+y+z=162\% \\3x+3y+z=291\% \end{array}\right..$

Для решения используем метод Крамера:

$\Delta=\left(\begin{array}{ccc}1&1&1\\2&1&1\\3&3&1\end{array}\right)=1*(1*1-3*1)-1*(2*1-3*1)+1*(2*3-3*1)=1-3-2+3+6-3=2.\\\Delta_y=\left(\begin{array}{ccc}1&100&1\\2&162&1\\3&291&1\end{array}\right)=1*(162*1- 291*1)-100*(2*1-3*1)+1*(2*291-3*162)=162-291-100*(2-3)+582-486=-129+100+96=67.\\y=\frac{\Delta_y}{\Delta} =\frac{67}{2}=33,5.$

Ответ: 33,5% от общего дохода семьи составляет зарплата жены.

Answer 2

Calculation of Wife's Salary as a Percentage of Total Family Income

To calculate the percentage of the wife's salary in the total family income, we need to analyze the given information. Let's break down the problem step by step:

1. The family consists of a husband, a wife, and their daughter who is a student. 2. If the husband's salary doubles, the total family income increases by 62%. 3. If the daughter's scholarship is reduced by one-third, the total family income decreases by 3%.

Let's assume the current family income is represented by X.

According to the given information, if the husband's salary doubles, the new family income will be 162% of the current income. Mathematically, this can be represented as:

1.62X = 2Y (Equation 1)

where Y represents the new family income.

Similarly, if the daughter's scholarship is reduced by one-third, the new family income will be 97% of the current income. Mathematically, this can be represented as:

0.97X = Z (Equation 2)

where Z represents the new family income.

Now, let's solve these equations to find the values of Y and Z.

From Equation 1, we can solve for Y:

Y = (1.62X) / 2

From Equation 2, we can solve for Z:

Z = 0.97X

To find the percentage of the wife's salary in the total family income, we need to calculate the ratio of the wife's salary to the total family income.

Let's assume the wife's salary is represented by W.

The percentage of the wife's salary in the total family income can be calculated as:

Percentage = (W / Y) * 100

Substituting the values of Y and W from the equations above, we get:

Percentage = (W / ((1.62X) / 2)) * 100

Simplifying further:

Percentage = (2W / (1.62X)) * 100

Now, let's calculate the percentage using the given information.

Please note that we do not have specific values for the husband's salary, wife's salary, or the current family income. Therefore, we cannot provide an exact percentage without these values. However, we can provide the general formula to calculate the percentage based on the given information.

Percentage = (2W / (1.62X)) * 100

Please substitute the actual values of the husband's salary, wife's salary, and the current family income into the formula to calculate the percentage.