Question

Вместе у Толи и у Вани было 100 лей.После того ,как каждый из них потратил половину своих денег ,у Толи осталось на 15 лей больше ,чем у Вани.Сколько денег изначально было у каждого?

Answer 1

Составим систему уравнений:
x лей было у Толи, y лей было у Вани
x+y=100
x/2-15=y/2
x-30=y
x-y+x+y=130
2x=130
x=130/2
x=65
y=65-30
y=35
Ответ: 65 лей было у Толи, 35 лей было у Вани

Answer 2

Task: Calculate the initial amount of money each person had.

To solve this problem, let's break it down step by step:

1. We know that together, Toli and Vanya had 100 lei. 2. After each of them spent half of their money, Toli had 15 lei more than Vanya.

Let's assume that Toli initially had x lei, and Vanya initially had y lei.

Based on the given information, we can create the following equations:

Equation 1: x + y = 100 (since together they had 100 lei) Equation 2: x/2 - y/2 = 15 (since Toli had 15 lei more than Vanya after spending half of their money)

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method:

From Equation 1, we can express x in terms of y: x = 100 - y

Substituting this value of x into Equation 2: (100 - y)/2 - y/2 = 15 (100 - y - y)/2 = 15 (100 - 2y)/2 = 15 100 - 2y = 30 -2y = 30 - 100 -2y = -70 y = -70/-2 y = 35

Now, we can substitute the value of y back into Equation 1 to find x: x + 35 = 100 x = 100 - 35 x = 65

Therefore, Toli initially had 65 lei, and Vanya initially had 35 lei.

Answer: Toli initially had 65 lei, and Vanya initially had 35 lei.