Question

Девочка купила тетради на сумму 60 тысяч рублей. А в другом магазине нашла тетради дешевле на 1000 рублей, и могла купить на 3 тетради больше. Сколько тетрадей купила девочка?

Answer 1

Пусть девочка купила х тетрадей. Тогда стоимость одной тетради в первом магазине равна (60000:х) рублей. На 60000 она могла купить в другом магазине (х+3) тетради. Тогда стоимость тетради в другом магазине равна (60000:(х+3)) рублей. По условию, тетради в другом магазине на 1000 рублей дешевле. Составляем уравнение:
$\frac{60000}{x+3} +1000= \frac{60000}{x}$
ОДЗ: х≠0, х≠-3.
$\frac{60000x}{x(x+3)} + \frac{1000x(x+3)}{x(x+3)} = \frac{60000(x+3)}{x(x+3)} |*x(x+3)\\60000x+1000x(x+3)=60000(x+3)|:1000\\60x+x(x+3)=60(x+3)\\60x+ x^{2} +3x-60x-180=0\\ x^{2} +3x-180=0\\D=b^2-4ac=9+4*180=729\ \textgreater \ 0\\ x_{1} = \frac{-b+ \sqrt{D} }{2a} = \frac{-3+ \sqrt{729} }{2} = \frac{-3+27}{2} =12\\ x_{2} = \frac{-b- \sqrt{D} }{2a} = \frac{-3- \sqrt{729} }{2} = \frac{-3-27}{2} =-15$
х не может быть равен -15, т.к. количество тетрадей не может быть отрицательным числом.
Значит, х=12 тетрадей - купила девочка.

Answer 2

Calculation of the Number of Notebooks Purchased

To calculate the number of notebooks the girl purchased, we need to consider the price difference between the two stores and the fact that she could buy 3 more notebooks with the money saved.

Let's assume that the girl initially bought the notebooks for 60,000 rubles in one store. In the other store, she found the same notebooks for 1,000 rubles cheaper. This means that she could buy the notebooks for 59,000 rubles in the second store.

To find out how many notebooks she could buy with the money saved, we need to calculate the difference in prices and divide it by the price of a single notebook.

The price difference between the two stores is 1,000 rubles, and she could buy 3 more notebooks with this money. Therefore, the price of a single notebook is 1,000 rubles divided by 3, which is 333.33 rubles (rounded to two decimal places).

To find the number of notebooks she could buy with the initial amount of money, we divide 60,000 rubles by the price of a single notebook (333.33 rubles):

Number of notebooks = 60,000 rubles / 333.33 rubles ≈ 180 notebooks.

Therefore, the girl purchased approximately 180 notebooks.

Please note that the above calculation assumes that the price of each notebook is the same in both stores and that there are no additional factors affecting the price or quantity of notebooks.