Question

За 3 стола і 4 стула заплатили 4700 грн. Скільки коштує 1 стол і 1 стул, якщо 2 стула дорожче одного стола на 100 грн?

Answer 1

Calculating the Cost of 1 Table and 1 Chair

To solve this problem, we can use a system of equations. Let's denote the cost of 1 table as x and the cost of 1 chair as y. We are given the following information:

1. 3 tables and 4 chairs cost 4700 UAH. 2. 2 chairs are more expensive than one table by 100 UAH.

We can express these statements as equations and solve for the values of x and y.

Setting Up the Equations

Let's use the given information to set up the equations:

1. The cost of 3 tables and 4 chairs is 4700 UAH: - Equation 1: 3x + 4y = 4700

2. The cost of 2 chairs is more than the cost of 1 table by 100 UAH: - Equation 2: 2y = x + 100

Solving the Equations

We can solve this system of equations to find the values of x and y.

First, let's solve Equation 2 for x: - x = 2y - 100

Now, substitute the value of x into Equation 1: - 3(2y - 100) + 4y = 4700 - 6y - 300 + 4y = 4700 - 10y - 300 = 4700 - 10y = 5000 - y = 500

Now that we have the value of y, we can find the value of x using the equation x = 2y - 100: - x = 2(500) - 100 - x = 1000 - 100 - x = 900

Answer

Therefore, the cost of 1 table is 900 UAH and the cost of 1 chair is 500 UAH.