Question

Вкладчик взял из сберкассы сначала 1/4 часть своих денег, потом 4/9 оставшихся и еще 640 тенге. После этого у него осталось на сберкнижке 3/20 всех его денег.Как велик был вклад? С подробным объяснением пожалуйста

Answer 1

1-1/4=3/4 всех денег осталось после 1го взятия
1-4/9=5/9 остатка осталось после 2го взятия
3/4*5/9=1/4*5/3=5/12 всех денег осталось после 2 го взятия
5/12-3/20=25/60-9/60=16/60=4/15 всех денег это 640 тг
640:4/15=640*15/4=160*15=2400тг был весь вклад

Уравнением:
х-весь вклад
х-1/4х-4/9(х-1/4х)-640=3/20х
х-1/4х-4/9*3/4х-640=3/20х
х-1/4х-1/3х-640=3/20х
х-1/4х-1/3х-3/20х=640
60/60х-15/60х-20/60х-9/60х=640
16/60х=640
х=640:16/60
х=640*60/16
х=2400

Answer 2

To solve this problem, we can break it down into steps. Let's go through each step:

1. The depositor initially withdrew 1/4 of their money from the savings account. 2. Then, they withdrew 4/9 of the remaining amount. 3. Finally, they withdrew an additional 640 tenge. 4. After these withdrawals, they were left with 3/20 of their total money in the savings account.

Let's solve for the deposit amount step by step:

Step 1: Withdrawing 1/4 of the money Let's assume the initial deposit amount is x tenge. The depositor withdrew 1/4 of x, which is (1/4)x.

Step 2: Withdrawing 4/9 of the remaining amount After the first withdrawal, the remaining amount in the account is (x - (1/4)x) = (3/4)x. The depositor then withdrew 4/9 of (3/4)x, which is (4/9) * (3/4)x = (1/3)x.

Step 3: Withdrawing an additional 640 tenge After the second withdrawal, the remaining amount in the account is ((3/4)x - (1/3)x) = (9/12)x - (4/12)x = (5/12)x. The depositor withdrew an additional 640 tenge, so we have the equation (5/12)x - 640 = (3/20)x.

Step 4: Solving for x To solve for x, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 60: 60 * [(5/12)x - 640] = 60 * (3/20)x 25x - 38400 = 9x

Simplifying the equation: 25x - 9x = 38400 16x = 38400 x = 2400

Therefore, the initial deposit amount was 2400 tenge.

I hope this explanation helps! Let me know if you have any further questions.