Question

Саше и Кате купили пальто ,ботинки и шапочки .Всего заплатили 750 грн . Каждая вещь ,купленная Саше стоит в 1,5 раз дороже ,чем этаже вишь , куплена для Кати . Пальто Саши стоит в 10 раз больше чем его шапка , и в 3 раза дороже чем ботики и шапка Кати . Сколько стоит каждая купленная вещь ?

Answer 1

Шапка Кати стоит x грн, шапка Саши 1,5x грн. Пальто Саши 10*1,5x = 15x грн, пальто Кати 15x:1,5 = 10x. Ботинки и шапка Кати стоят 15x:3 = 5x грн. Ботинки Кати 5x-x = 4x грн, ботинки Саши 4x*1,5 = 6x грн. Всё вместе 750 грн.
x+1,5x+10x+15x+4x+6x = 750
37,5x = 750
x = 20
Шапка Кати 20 грн, шапка Саши 20*1,5 = 30 грн, пальто Кати 10*20 = 200 грн, пальто Саши 15*20 = 300 грн, ботинки Кати 4*20 = 80 грн, ботинки Саши 6*20 = 120 грн.

Answer 2

Problem Analysis

We are given that Sasha and Katya bought coats, boots, and hats, and the total cost was 750 UAH. Each item bought for Sasha is 1.5 times more expensive than the same item bought for Katya. Sasha's coat is 10 times more expensive than his hat and 3 times more expensive than Katya's boots and hat. We need to determine the cost of each item.

Solution

Let's assign variables to the cost of each item: - Let's denote the cost of Katya's hat as x. - The cost of Katya's boots will be y. - The cost of Sasha's hat will be 1.5x. - The cost of Sasha's boots will be 1.5y. - The cost of Sasha's coat will be 10(1.5x) = 15x.

We know that the total cost of all the items is 750 UAH. Therefore, we can write the equation:

x + y + 1.5x + 1.5y + 15x = 750

Simplifying the equation:

18x + 2.5y = 750

To solve this equation, we need another equation. We can use the information that each item bought for Sasha is 1.5 times more expensive than the same item bought for Katya. This gives us the equation:

1.5x = y

Now we have a system of two equations:

18x + 2.5y = 750 (Equation 1) 1.5x = y (Equation 2)

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

Solution Steps

1. Substitute Equation 2 into Equation 1 to eliminate y: 18x + 2.5(1.5x) = 750 Simplifying: 18x + 3.75x = 750 Combining like terms: 21.75x = 750 Solving for x: x = 750 / 21.75 Calculating: x ≈ 34.48

2. Substitute the value of x back into Equation 2 to find y: 1.5(34.48) = y Calculating: y ≈ 51.72

3. Calculate the cost of each item: - Katya's hat (x): ≈ 34.48 UAH - Katya's boots (y): ≈ 51.72 UAH - Sasha's hat (1.5x): ≈ 51.72 UAH - Sasha's boots (1.5y): ≈ 77.58 UAH - Sasha's coat (15x): ≈ 517.20 UAH

Answer

The cost of each item is approximately: - Katya's hat: ≈ 34.48 UAH - Katya's boots: ≈ 51.72 UAH - Sasha's hat: ≈ 51.72 UAH - Sasha's boots: ≈ 77.58 UAH - Sasha's coat: ≈ 517.20 UAH

Please note that these values are approximate due to rounding.

Let me know if there is anything else I can help you with!