Question

Помогите решить задачу с помощью систем.2 ручки и 3 карандаша стоят 35 руб.,а 3 ручки и 2 карандаша стоят 40 руб. Сколько стоят 1 карандаш и 1 ручка? Сколько стоят 5 ручек и 6 карандашей?

Answer 1

Х р. - стоит 1 ручка
у р. - стоит 1 карандаш
Составляем систему уравнений:
2х+3у=35
3х+2у=40
_______________
2х=35-3у
3х+2у=40
_______________
х=(35-3у)/2
3х+2у=40
_______________
х=(35-3у)/2
3(35-3у)/2 +2у=40
________________
х=(35-3у)/2
3(35-3у)+2·2у=40·2
_________________
х=(35-3у)/2
105-9у+4у=80
_________________
х=(35-3у)/2
-5у=80-105
_________________
х=(35-3у)/2
5у=25
________________
х=(35-3у)/2
у=5
_________________
х=(35-3·5)/2
у=5
_________________
х=10р.- стоит 1 ручка
у=5р. - стоит 1 карандаш
5·10+6·5=80р. - стоят 5 ручек и 6 карандашей

Answer 2

Problem Analysis

To solve this problem, we can set up a system of equations based on the given information. Let's assume the cost of one pen is P and the cost of one pencil is C. We can then set up the following equations:

Equation 1: 2P + 3C = 35 (equation based on the cost of 2 pens and 3 pencils) Equation 2: 3P + 2C = 40 (equation based on the cost of 3 pens and 2 pencils)

We can solve this system of equations to find the values of P and C, which will give us the cost of one pen and one pencil.

Solving the System of Equations

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

Multiplying Equation 1 by 3 and Equation 2 by 2, we get:

Equation 3: 6P + 9C = 105 Equation 4: 6P + 4C = 80

Subtracting Equation 4 from Equation 3, we get:

(6P + 9C) - (6P + 4C) = 105 - 80 5C = 25 C = 5

Substituting the value of C into Equation 1, we get:

2P + 3(5) = 35 2P + 15 = 35 2P = 35 - 15 2P = 20 P = 10

Therefore, the cost of one pencil is 5 rubles and the cost of one pen is 10 rubles.

Calculating the Cost of 5 Pens and 6 Pencils

To calculate the cost of 5 pens and 6 pencils, we can simply multiply the cost of one pen by 5 and the cost of one pencil by 6, and then add the results:

Cost of 5 pens = 5 * 10 = 50 rubles Cost of 6 pencils = 6 * 5 = 30 rubles

Therefore, the cost of 5 pens and 6 pencils is 80 rubles.

I hope this helps! Let me know if you have any further questions.