Question

До свята купили цукерок у 3 рази більше, ніж печива. Визначте ціну цукерок і печива, якщо 1 кг цукерок на 30,5 грн дорожчий за 1 кг печива. ​

Answer 1

До свята купили цукерок у 3 рази більше, ніж печива. Визначте ціну цукерок і печива, якщо 1 кг цукерок на 30,5 грн дорожчий за 1 кг печива.

1) Нехай х – вартість печива, тоді 3х + 3 • 30,5 – вартість цукерок;

3х – х = 3 • 30,5

2х = 91,5

х = 91,5 : 2

х = 45,75 (грн) – ціна печива.

2) 45,75 + 30,5 = 76,25 (грн) – ціна цукерок.

Відповідь: ціна печива 45,75 грн, цукерок – 76,25 грн.

Answer 2

Problem Analysis

We are given that the quantity of candies is three times greater than the quantity of cookies. We need to determine the prices of the candies and cookies, given that the price of 1 kg of candies is 30.5 UAH more expensive than 1 kg of cookies.

Solution

Let's assume the price of 1 kg of cookies is x UAH. Since the price of 1 kg of candies is 30.5 UAH more expensive than 1 kg of cookies, the price of 1 kg of candies would be x + 30.5 UAH.

Since the quantity of candies is three times greater than the quantity of cookies, we can set up the following equation:

3x = x + 30.5

Simplifying the equation, we get:

2x = 30.5

Dividing both sides of the equation by 2, we find:

x = 15.25

Therefore, the price of 1 kg of cookies is 15.25 UAH, and the price of 1 kg of candies is 15.25 + 30.5 = 45.75 UAH.

Answer

The price of cookies is 15.25 UAH per 1 kg, and the price of candies is 45.75 UAH per 1 kg.