Question

В первую неделю отпускного путешествия друзья израсходовали на 60 тенге меньше, чем 2/5 количества взятых с собой денег, во вторую неделю 1/3 остатка и еще на билеты в театр 12 тенге, в третью неделю 3/5 нового остатка и еще на морские прогулки 31 тенге 20 тиын, после чего у них осталось 420 тенге Сколько денег было израсходовано за три недели путешествия?

Answer 1

Ответ:

1)60:5•2=24

2)12:3•2=8

3)31+30=51

4)24+8+51=83

5)420-83=337

Ответ:337

Answer 2

To calculate the total amount of money spent during the three-week vacation, we need to break down the expenses for each week and then add them up.

Week 1:

The friends spent 60 tenge less than 2/5 of the money they brought with them. Let's assume they brought x tenge with them. Therefore, the amount spent in the first week can be calculated as: (2/5)x - 60 tenge.

Week 2:

In the second week, they spent 1/3 of the remaining amount, which is (3/5)x - 60 tenge. Additionally, they spent 12 tenge on theater tickets. Therefore, the total amount spent in the second week is: (3/5)x - 60 tenge + 12 tenge.

Week 3:

In the third week, they spent 3/5 of the new remaining amount, which is (3/5)((3/5)x - 48 tenge). Additionally, they spent 31 tenge and 20 tiyn on sea walks. Therefore, the total amount spent in the third week is: (3/5)((3/5)x - 48 tenge) + 31 tenge + 20 tiyn.

Remaining Amount:

After the three weeks, they had 420 tenge left.

To find the total amount spent during the three-week vacation, we need to sum up the expenses for each week and subtract it from the initial amount they brought with them.

Let's calculate it step by step:

1. Subtract the expenses of the third week from the remaining amount: 420 tenge = (3/5)((3/5)x - 48 tenge) + 31 tenge + 20 tiyn.

2. Simplify the equation: 420 tenge = (9/25)x - 86.4 tenge + 31 tenge + 20 tiyn.

3. Convert the tiyn to tenge: 420 tenge = (9/25)x - 86.4 tenge + 31 tenge + 0.2 tenge.

4. Combine like terms: 420 tenge = (9/25)x - 55.2 tenge.

5. Add 55.2 tenge to both sides of the equation: 420 tenge + 55.2 tenge = (9/25)x.

6. Simplify: 475.2 tenge = (9/25)x.

7. Multiply both sides of the equation by (25/9) to isolate x: x = (475.2 tenge) * (25/9).

8. Calculate x: x ≈ 1316.67 tenge.

Now that we know the initial amount they brought with them (x), we can calculate the total amount spent during the three-week vacation.

Total Amount Spent:

To calculate the total amount spent, we need to sum up the expenses for each week:

Week 1: (2/5)x - 60 tenge. Week 2: (3/5)x - 60 tenge + 12 tenge. Week 3: (3/5)((3/5)x - 48 tenge) + 31 tenge + 20 tiyn.

Let's substitute the value of x we calculated earlier:

Week 1: (2/5)(1316.67 tenge) - 60 tenge. Week 2: (3/5)(1316.67 tenge) - 60 tenge + 12 tenge. Week 3: (3/5)((3/5)(1316.67 tenge) - 48 tenge) + 31 tenge + 20 tiyn.

Now we can calculate the total amount spent by adding up the expenses for each week:

Total Amount Spent = Week 1 + Week 2 + Week 3.

Please note that the tiyn should be converted to tenge before performing the calculations.