Question

4 карандаша и 3 тетради стоят 54 руб..., а 2 карандаша и 2 тетради - 34 р. Сколько стоят 6 таких карандашей, и 5 таких тетрадей?

Answer 1

Problem Analysis

We are given the information that 4 pencils and 3 notebooks cost 54 rubles, and that 2 pencils and 2 notebooks cost 34 rubles. We need to determine the cost of 6 pencils and 5 notebooks.

Solution

Let's assign variables to the unknowns: let `p` represent the cost of one pencil and `n` represent the cost of one notebook.

From the given information, we can set up the following equations:

Equation 1: 4p + 3n = 54 Equation 2: 2p + 2n = 34

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

From Equation 2, we can express `p` in terms of `n`:

2p = 34 - 2n p = (34 - 2n) / 2 p = 17 - n

Now we substitute this expression for `p` into Equation 1:

4(17 - n) + 3n = 54 68 - 4n + 3n = 54 68 - n = 54 n = 68 - 54 n = 14

Substituting the value of `n` back into Equation 2 to find `p`:

2p + 2(14) = 34 2p + 28 = 34 2p = 34 - 28 2p = 6 p = 6 / 2 p = 3

Therefore, the cost of one pencil is 3 rubles and the cost of one notebook is 14 rubles.

To find the cost of 6 pencils, we multiply the cost of one pencil by 6:

6 * 3 = 18 rubles

To find the cost of 5 notebooks, we multiply the cost of one notebook by 5:

5 * 14 = 70 rubles

Therefore, 6 pencils and 5 notebooks cost a total of 88 rubles.

Answer

The cost of 6 pencils and 5 notebooks is 88 rubles.