Question

Світлана купила 9 олівців (-і) за ціною y грн за олівець, а Тетяна — 2 ручок (-ки) за ціною в 1,4 разів (-и) більшою, ніж ціна за олівець. Після цього в дівчаток залишилося 48,5 грн. Яка сума грошей була в дівчаток спочатку? Склади вираз і спрости його.

Answer 1

Відповідь:

48,7=7х+4*(1,2х)

48,7=7х+4,8х

48,7=11,8х

х=48,7:11,8

х=4,1

Answer 2

Problem Analysis

We are given that Svitlana bought 9 pencils at a price of y hryvnias per pencil, and Tetiana bought 2 pens at a price 1.4 times higher than the price of a pencil. After their purchases, both girls had 48.5 hryvnias left. We need to determine the initial amount of money the girls had.

Solution

Let's solve this problem step by step.

1. Let's start by expressing the total cost of Svitlana's pencils. Since she bought 9 pencils at a price of y hryvnias per pencil, the total cost of her pencils is 9y hryvnias.

2. Now, let's express the total cost of Tetiana's pens. We are given that the price of a pen is 1.4 times higher than the price of a pencil. Therefore, the price of a pen is 1.4y hryvnias. Since Tetiana bought 2 pens, the total cost of her pens is 2 * 1.4y = 2.8y hryvnias.

3. We are also given that after their purchases, both girls had 48.5 hryvnias left. Therefore, the total amount of money they spent is the difference between their initial amount of money and the amount they have left. Let's denote the initial amount of money they had as X hryvnias. The total amount they spent is X - 48.5 hryvnias.

4. Now, let's set up an equation to represent the total amount they spent. The total amount they spent is equal to the sum of the total cost of Svitlana's pencils and the total cost of Tetiana's pens. Therefore, we have the equation:

X - 48.5 = 9y + 2.8y

5. Simplifying the equation, we get:

X - 48.5 = 11.8y

6. Finally, let's solve the equation for X, the initial amount of money the girls had:

X = 11.8y + 48.5

Answer

The initial amount of money the girls had is 11.8y + 48.5 hryvnias.

Note: The answer is expressed in terms of y, the price of a pencil.