Question

у маши была некоторая сумма денег.На первую покупку она потратил 1/3 всей суммы,а на вторую 1/2 остатка.после чего у неёосталось 1200 рублей.сколько рублей было у маши первоночально?

Answer 1

было х

потратила на первую покупку 1/3х

на вторую покупку 1/2(х-1/3х)

осталось 1200

составим уравнение

х=1/3х+1/2(х-1/3х)+1200

х-1/3х-0,5(х-1/3х)-1200=0

2/3х-0,5*2/3х-1200=0

1/3х=1200

х-1200:1/3

х=3600 всего было денег

 

 

 

Answer 2

Problem Analysis

To solve this problem, we need to determine the initial amount of money that Masha had before making the two purchases. We are given that Masha spent 1/3 of the total amount on the first purchase and 1/2 of the remaining amount on the second purchase. After these two purchases, Masha had 1200 rubles left.

Solution

Let's assume the initial amount of money that Masha had is x rubles.

1. Masha spent 1/3 of the total amount on the first purchase, which is (1/3)x rubles. 2. After the first purchase, Masha had (2/3)x rubles remaining. 3. Masha then spent 1/2 of the remaining amount on the second purchase, which is (1/2)(2/3)x = (1/3)x rubles. 4. After the second purchase, Masha had (2/3)x - (1/3)x = (1/3)x rubles remaining. 5. We are given that Masha had 1200 rubles left, so we can set up the equation (1/3)x = 1200 and solve for x.

Let's solve the equation:

(1/3)x = 1200

Multiplying both sides of the equation by 3:

x = 1200 * 3

x = 3600

Therefore, the initial amount of money that Masha had was 3600 rubles.

Answer

Masha initially had 3600 rubles.