Question

За 8 ракеток и 10 мячей заплатили 4560 р. Во время распродажи цена на ракетки была снижена на 25%, а на мячи на 10% и такая покупка стала стоить 3780 р. Найдите первоначальную цену каждого вида товараМОЖНО РАЗВЕРНУТЫЙ ОТВЕТ, ПОЖАЛУЙСТА!

Answer 1

8х+10у=4560
8*0.75+10*0.9у=3780

х=270
у=240
ответ:ракетка 270р. мяч 240р.

Answer 2

Problem Analysis

We are given the information that 8 rackets and 10 balls were purchased for a total of 4560 rubles. During a sale, the price of rackets was reduced by 25% and the price of balls was reduced by 10%. After the sale, the total cost of the purchase was 3780 rubles. We need to find the initial price of each item.

Solution

Let's assume the initial price of a racket is 'x' rubles and the initial price of a ball is 'y' rubles.

According to the given information, the total cost of 8 rackets and 10 balls before the sale was 4560 rubles. So, we can write the equation:

8x + 10y = 4560 ---(1)

After the sale, the total cost of the purchase was 3780 rubles. The price of rackets was reduced by 25% and the price of balls was reduced by 10%. So, the new price of a racket is 75% of the initial price (0.75x) and the new price of a ball is 90% of the initial price (0.9y). We can write the equation:

8(0.75x) + 10(0.9y) = 3780 ---(2)

Now, we can solve these two equations to find the initial prices of the rackets and balls.

Solving the Equations

Let's solve the equations (1) and (2) using the substitution method.

From equation (1), we can express 'x' in terms of 'y':

x = (4560 - 10y) / 8 ---(3)

Substituting the value of 'x' from equation (3) into equation (2), we get:

8(0.75)((4560 - 10y) / 8) + 10(0.9y) = 3780

Simplifying the equation:

3420 - 6y + 9y = 3780 3y = 360 y = 120

Substituting the value of 'y' back into equation (3), we can find the value of 'x':

x = (4560 - 10(120)) / 8 x = (4560 - 1200) / 8 x = 3360 / 8 x = 420

Answer

The initial price of each racket was 420 rubles and the initial price of each ball was 120 rubles.

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