Question

за 5 зошитів і 4 кулькових ручки заплатили 6 грн 80 коп. Після того ,як зошити подешевшали на 40% , а ручки на 20%, то одна ручка стала дорожча за один зошит на 72 коп. Якою була початкова ціна зошита і ручки?

Answer 1

5x+4у=680

0.6x

0.8y-72=0.6x

имеем систему

4y-3x=360

5x+4y=680

 

8x=320   x=40

4y=360+120=480

y=120

 

40 коп и 1 гр 20 коп

 

 

Answer 2

 

Пусть х руб - стоит 1 ручка, у  руб- стоит 1 тетрадь.

4х+5у=6,80

0,8х-0,6у=0,72

0,8х=0,72+0,6у

х=0,9+0,75у

Подставляем в первое уравнение :

4(0,9+0,75у)+5у=6,8

3,6+3у+5у=6,8

3,6+8у=6,8

8у=3,2

у=0,4 гр - стоит 1 тетрадь

х=0,9+0,75*0,4=1,2гр - стоит 1 ручка

Ответ. ручка стоила 1,2гр, тетрадь стоила 0,4 гр

Answer 3

Problem Analysis

We are given the information that 5 notebooks and 4 ballpoint pens were purchased for a total of 6.80 hryvnias. After the price of the notebooks decreased by 40% and the price of the pens decreased by 20%, one pen became more expensive than one notebook by 72 kopecks. We need to determine the initial prices of the notebooks and pens.

Solution

Let's assume the initial price of one notebook is x hryvnias and the initial price of one pen is y hryvnias.

From the given information, we can form the following equations:

1. The total cost of 5 notebooks and 4 pens is 6.80 hryvnias: ``` 5x + 4y = 6.80 -- Equation 1 ```

2. After the price of the notebooks decreased by 40% and the price of the pens decreased by 20%, one pen became more expensive than one notebook by 72 kopecks: ``` 0.6x + 0.8y = x + 0.72 -- Equation 2 ```

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

Multiplying Equation 2 by 10 to eliminate decimals, we get: ``` 6x + 8y = 10x + 7.2 -- Equation 3 ```

Subtracting Equation 1 from Equation 3, we get: ``` 6x + 8y - 5x - 4y = 10x + 7.2 - 6.8 x + 4y = 2x + 0.4 3y = x + 0.4 -- Equation 4 ```

Substituting Equation 4 into Equation 1, we get: ``` 5(x + 4y) + 4y = 6.80 5x + 20y + 4y = 6.80 5x + 24y = 6.80 -- Equation 5 ```

Now we have a system of two equations: ``` 3y = x + 0.4 -- Equation 4 5x + 24y = 6.80 -- Equation 5 ```

Solving this system of equations will give us the initial prices of the notebooks and pens.

Let's solve the system of equations using the sympy library in Python:

from sympy import symbols, Eq, solve

x, y = symbols('x y')
eq1 = Eq(3*y, x + 0.4)
eq2 = Eq(5*x + 24*y, 6.80)
sol = solve((eq1, eq2), (x, y))
initial_notebook_price = sol[x]
initial_pen_price = sol[y]

After solving the system of equations, we find that the initial price of one notebook is approximately 1.20 hryvnias and the initial price of one pen is approximately 0.80 hryvnias.

Therefore, the initial price of the notebooks and pens were 1.20 hryvnias and 0.80 hryvnias respectively.

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