Question

За 7 ручек уплатили на 1410 р. меньше, чем за 15 тетрадей. Определите цену одной ручки и одной тетради, учитывая, что 5 ручек стоят столько же, сколько 4 тетради. Решите системой

Answer 1

Х- одна ручка у-цена 1 тетради
15у-7х=1410
5х=4у

15у-7х=1410
х=4у:5
 
15у-7*4у/5=1410
15у-28у/5=1410
15у-5 3/5*у=1410
9 2/5*у=1410
у=1410: 9 2/5
у=1410*5/47=30*5=150р  стоит 1 тетрадь
х=4*150:5=120 р стоит 1 ручка

Answer 2

Problem Analysis

We are given the information that the cost of 7 pens is 1410 rubles less than the cost of 15 notebooks. We also know that the cost of 5 pens is equal to the cost of 4 notebooks. We need to determine the price of one pen and one notebook.

Solution

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

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

Equation 1: 7x = 15y - 1410 (the cost of 7 pens is 1410 rubles less than the cost of 15 notebooks)

Equation 2: 5x = 4y (the cost of 5 pens is equal to the cost of 4 notebooks)

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

Substitution Method

We can solve Equation 2 for x in terms of y and substitute it into Equation 1.

From Equation 2, we have: x = (4/5)y

Substituting this value of x into Equation 1, we get: 7(4/5)y = 15y - 1410

Simplifying the equation: (28/5)y = 15y - 1410

Multiplying both sides of the equation by 5 to eliminate the fraction: 28y = 75y - 7050

Subtracting 75y from both sides of the equation: -47y = -7050

Dividing both sides of the equation by -47: y = 150

Now that we have the value of y, we can substitute it back into Equation 2 to find the value of x.

From Equation 2, we have: x = (4/5)y x = (4/5)(150) x = 120

Therefore, the price of one pen is 120 rubles and the price of one notebook is 150 rubles.

Answer

The price of one pen is 120 rubles and the price of one notebook is 150 rubles.