Question

Стіл і стілець коштують разом 1500 грн Після того як стіл полегевшав на 20 відсотків , а стілець подорожчав на 20 відсотків , вони стали коштувати 1320 грн Знайти початкову ціну стола і стільця окремо.

Answer 1

20% - 0,2
х - стоил стул
у - стоил стол
х+0,2х -стал стоить стул
у-0,2у - стал стоить стол

х+у=1500
х+0,2х+у-0,2у=1320

х+у=1500
1,2х+0,8у=1320  Решим систему

Из первого уравнения
х=1500-у  Подставим во второе уравнение

1,2(1500-у)+0,8у=1320
1800-1,2у+0,8у=1320
1800-1320=1,2у-0,8у
480=0,4у
у=480:0,4
у=1200 (грн) стоил стол
1500-1200=300 (грн) стоил стул
Ответ: начальная цена стола - 1200 гривен, а стула - 300 гривен

Проверка:
1200+300=1500
1200-1200*0,2=1200-240=960
300+300*0,2=300+60=360
960+360=1320 (что соответствует условию задачи)

Answer 2

Problem Analysis

We are given that the combined cost of a table and a chair is 1500 UAH. After the table decreases in price by 20% and the chair increases in price by 20%, the combined cost becomes 1320 UAH. We need to find the initial prices of the table and the chair separately.

Solution

Let's assume the initial price of the table is x UAH and the initial price of the chair is y UAH.

According to the given information, we have the following equations:

1. x + y = 1500 (equation 1) - The combined cost of the table and the chair is 1500 UAH. 2. 0.8x + 1.2y = 1320 (equation 2) - After the table decreases in price by 20% and the chair increases in price by 20%, the combined cost becomes 1320 UAH.

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method.

Multiplying equation 1 by 1.2, we get:

1.2x + 1.2y = 1800 (equation 3)

Now, subtract equation 2 from equation 3:

(1.2x + 1.2y) - (0.8x + 1.2y) = 1800 - 1320

0.4x = 480

Divide both sides of the equation by 0.4:

x = 1200

Substituting the value of x into equation 1, we can find the value of y:

1200 + y = 1500

y = 1500 - 1200

y = 300

Therefore, the initial price of the table is 1200 UAH and the initial price of the chair is 300 UAH.

Answer

The initial price of the table is 1200 UAH and the initial price of the chair is 300 UAH.