Question

За 2 стола и 6 стульев заплатили 1520 грн. После того , как столы подешевели на 10 % , а стулья на 20% , за один стол и два стула заплатили 552 грн . Какова была начальная цена одного стола и одного стула ?

Answer 1

Х-нач.цена стола,0,9х-цена после уценки
у-нач.цена стула,0,8х-цена после уценки
2х+6у=1520⇒х+3у=760⇒х=760-3у
0,9х+1,6у=552
0,9(760-3у)+1,6у=552
684-2,7у+1,6у=552
-1,1у=-132
у=120-нач.цена стула
х=760-3*120=760-360=400-нач.цена стола

Answer 2

Problem Analysis

We are given the information that 2 tables and 6 chairs were purchased for a total of 1520 UAH. After the tables decreased in price by 10% and the chairs decreased in price by 20%, one table and two chairs were purchased for a total of 552 UAH. We need to determine the initial price of one table and one chair.

Solution

Let's assume the initial price of one table is T UAH and the initial price of one chair is C UAH.

From the given information, we can form two equations:

Equation 1: 2T + 6C = 1520 (total cost of 2 tables and 6 chairs is 1520 UAH) Equation 2: T + 2C = 552 (total cost of 1 table and 2 chairs is 552 UAH)

We can solve these equations to find the values of T and C.

Solving the Equations

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

From Equation 2, we can express T in terms of C: T = 552 - 2C

Substituting this value of T into Equation 1, we get: 2(552 - 2C) + 6C = 1520 1104 - 4C + 6C = 1520 2C = 1520 - 1104 2C = 416 C = 416 / 2 C = 208

Now, substitute the value of C back into Equation 2 to find T: T + 2(208) = 552 T + 416 = 552 T = 552 - 416 T = 136

Answer

The initial price of one table was 136 UAH and the initial price of one chair was 208 UAH.

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