Question

Если петя даст саше 100рублей,то у друзей денег будет поровну а если саша даст пете 100рублей то у пети будет в 9 раз больше чем у саши. сколько денег у каждого?

Answer 1

P-деньги пети
S-деньги саши
$\left \{ {{P-100=S+100} \atop {9*(S-100)=P+100}} \right.$
$\left \{ {{P=S+200} \atop {P=9*(S-100)-100}} \right.$
$S+200=9S-100$
$8S=1200$
$C= \frac{600}{4} =150$руб
$P=S+200=350$руб

Answer 2

Problem Analysis

We have two friends, Petya and Sasha. If Petya gives Sasha 100 rubles, then the friends will have an equal amount of money. However, if Sasha gives Petya 100 rubles, then Petya will have 9 times more money than Sasha. We need to determine how much money each friend has.

Solution

Let's assume Petya has x rubles and Sasha has y rubles.

According to the given information: 1. If Petya gives Sasha 100 rubles, then the friends will have an equal amount of money. 2. If Sasha gives Petya 100 rubles, then Petya will have 9 times more money than Sasha.

Based on these conditions, we can set up the following equations:

Equation 1: x - 100 = y + 100 (Petya gives 100 rubles to Sasha)

Equation 2: x + 100 = 9 * (y - 100) (Sasha gives 100 rubles to Petya)

Now, let's solve these equations to find the values of x and y.

Solving the Equations

To solve the equations, we can use a method called substitution. We'll solve Equation 1 for x and substitute it into Equation 2.

From Equation 1, we have: x = y + 200

Substituting this value of x into Equation 2, we get:

y + 200 + 100 = 9 * (y - 100)

Simplifying the equation:

y + 300 = 9y - 900

8y = 1200

y = 150

Substituting the value of y back into Equation 1, we get:

x = 150 + 200

x = 350

Answer

Therefore, Petya has 350 rubles and Sasha has 150 rubles.