Question

У друзей 675 рублей на двоих. Если один из них отдаст другому 100 рублей, то у него останется в 1,5 раза меньше денег, чем станет у другого. Сколько денег у каждого?

Answer 1

1,5(x-100)=775-x
1,5x-150=775-x
1,5x+x=775+150
2,5x=925
x=370(р)-первый
675-370=305(р)-второй

Answer 2

Problem Analysis

We are given that two friends have a total of 675 rubles. If one of them gives the other 100 rubles, the person who gave the money will have 1.5 times less money than the other person. We need to determine how much money each person has.

Solution

Let's assume that the first friend has x rubles and the second friend has y rubles.

According to the given information, we have the following equations: 1. x + y = 675 (the total amount of money the two friends have) 2. x - 100 = 1.5 * (y + 100) (if one friend gives the other 100 rubles, the giver will have 1.5 times less money than the receiver)

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

Solving the Equations

Let's solve the system of equations using substitution or elimination method.

From equation 1, we have: x = 675 - y

Substituting this value of x into equation 2, we get: 675 - y - 100 = 1.5 * (y + 100)

Simplifying the equation: 575 - y = 1.5y + 150

Combining like terms: 2.5y = 425

Dividing both sides by 2.5: y = 170

Substituting the value of y back into equation 1, we get: x + 170 = 675 x = 505

Answer

Therefore, the first friend has 505 rubles and the second friend has 170 rubles.

Verification

Let's verify if our solution satisfies the given conditions.

According to the given information, if one friend gives the other 100 rubles, the giver will have 1.5 times less money than the receiver.

Let's check if this condition holds true: - If the first friend gives 100 rubles to the second friend, the first friend will have 505 - 100 = 405 rubles. - The second friend will have 170 + 100 = 270 rubles. - Is 405 equal to 1.5 times 270? Yes, it is.

Therefore, our solution is verified and correct.

Conclusion

The first friend has 505 rubles and the second friend has 170 rubles.