Question

Карандаш и ручка вместе стоят 8 руб а пять карандашей и две ручки стоят 25 руб. Сколько стоит карандаш и сколько стоит ручка?

Answer 1

3y=9
у=5рублей стоила ручка карандаш принимаем за х, ручку за у.2x+5y=25х=8-у=8-5=3рубля стоил карандашПусть х - стоимость ручки, а у - стоимость канадраша, составим систему уравнений:2(8-y)+5y=25Выразим из первого уравнения х=8-y и подставим это значение вместо х во второе уравнение:5*(8-у)+2у=25Если y=3, то ручка стоит х=8-y=8-3=5 рублей.Ответ: ручка - 5 руб., канадаш - 3 рубля.40-5у+2у=25
-3у=-15х+у=8
3y=25-16х+y=8
16-2y+5y=25
х=8-у
y=3 рубля стоит карандаш.y=9/3 y=3

Answer 2

Problem Analysis

We are given that a pencil and a pen together cost 8 rubles, and that five pencils and two pens together cost 25 rubles. We need to determine the individual prices of a pencil and a pen.

Solution

Let's assume the price of a pencil is x rubles and the price of a pen is y rubles.

From the given information, we can form two equations:

1. Equation 1: "A pencil and a pen together cost 8 rubles" - This can be expressed as: x + y = 8.

2. Equation 2: "Five pencils and two pens together cost 25 rubles" - This can be expressed as: 5x + 2y = 25.

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

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 substitution.

From Equation 1, we can express x in terms of y: - x = 8 - y

Substituting this value of x into Equation 2, we get: - 5(8 - y) + 2y = 25 - 40 - 5y + 2y = 25 - -3y = -15 - y = 5

Now, substituting the value of y back into Equation 1, we get: - x + 5 = 8 - x = 3

Answer

Therefore, the price of a pencil is 3 rubles and the price of a pen is 5 rubles.