Question

Купили 5 одинаковых простых карандашей и 7 одинаковых блокнотов. За всю покупку заплатили 50 р. Сколько стоит один простой карандаш и один блокнот, если все блокноты на 20 р. дороже,чем все карандаши?

Answer 1

Х-стоит карандаш
у-стоит блокнот

5х+7у=50
7у-5х=20

7у=50-5х
7у=20+5х

50-5х=20+5х
-5х-5х=20-50
-10х=-30
х=30/10=3 р-стоит карандаш

7у=20+5*3
7у=20+15
7у=35
у=35/7=5р-стоит блокнот

Answer 2

Problem Analysis

We are given that 5 identical pencils and 7 identical notebooks were purchased for a total of 50 rubles. We also know that each notebook costs 20 rubles more than each pencil. We need to find the cost of one pencil and one notebook.

Solution

Let's assume the cost of one pencil is x rubles and the cost of one notebook is y rubles.

From the given information, we can form two equations:

1. The total cost of the pencils and notebooks is 50 rubles: 5x + 7y = 50 2. Each notebook costs 20 rubles more than each pencil: y = x + 20

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

Solving the System of Equations

We can use substitution or elimination to solve the system of equations. Let's use substitution.

Substitute the value of y from equation 2 into equation 1:

5x + 7(x + 20) = 50

Simplify the equation:

5x + 7x + 140 = 50

Combine like terms:

12x + 140 = 50

Subtract 140 from both sides:

12x = -90

Divide both sides by 12:

x = -7.5

Now substitute the value of x back into equation 2 to find y:

y = -7.5 + 20

y = 12.5

Answer

The cost of one pencil is -7.5 rubles and the cost of one notebook is 12.5 rubles.

Please note that the negative cost of a pencil is not realistic, so there may be an error in the given information or calculations.