Question

Зина удалила все прочитанные письма. Если раньше во входящих было трёхзначное число сообщений, то теперь оно стало двузначным, причём таким, как если бы из исходного числа просто убрали первую цифру. В результате писем во входящих стало в 15 раз меньше, чем было. Сколько их там теперь?

Answer 1

Пусть исходное число равно 100a + b, после удаления прочитанных b. По условию число писем уменьшалось в 15 раз, поэтому
100a + b = 15b
100a = 14b
50a = 7b

a - цифра, 50a делится на 7, значит, a = 7. Тогда b = 50 * 7 / 7 = 50.

Ответ. сейчас во входящих 50 писем.

(было 750, стало 50, уменьшилось в 15 раз).

Answer 2

Problem Analysis

Zina deleted all the read emails from her inbox. Previously, there were three-digit numbers of messages in her inbox, but now there are two-digit numbers. The new numbers are obtained by removing the first digit from the original numbers. The number of emails in her inbox has decreased by a factor of 15. We need to determine the current number of emails in her inbox.

Solution

Let's assume the original number of emails in Zina's inbox was represented by a three-digit number, ABC. According to the problem, the new number of emails is obtained by removing the first digit, resulting in a two-digit number, BC.

We are given that the new number of emails is 15 times smaller than the original number. Mathematically, we can express this as:

BC = ABC / 15

To find the current number of emails in Zina's inbox, we need to determine the value of BC.

Calculation

To calculate the current number of emails in Zina's inbox, we need to find the value of BC.

Let's consider the possible values of BC from 10 to 99 and check if any of them satisfy the equation BC = ABC / 15.

For BC = 10: 10 = ABC / 15 ABC = 150

For BC = 11: 11 = ABC / 15 ABC = 165

For BC = 12: 12 = ABC / 15 ABC = 180

For BC = 13: 13 = ABC / 15 ABC = 195

For BC = 14: 14 = ABC / 15 ABC = 210

For BC = 15: 15 = ABC / 15 ABC = 225

For BC = 16: 16 = ABC / 15 ABC = 240

For BC = 17: 17 = ABC / 15 ABC = 255

For BC = 18: 18 = ABC / 15 ABC = 270

For BC = 19: 19 = ABC / 15 ABC = 285

For BC = 20: 20 = ABC / 15 ABC = 300

For BC = 21: 21 = ABC / 15 ABC = 315

For BC = 22: 22 = ABC / 15 ABC = 330

For BC = 23: 23 = ABC / 15 ABC = 345

For BC = 24: 24 = ABC / 15 ABC = 360

For BC = 25: 25 = ABC / 15 ABC = 375

For BC = 26: 26 = ABC / 15 ABC = 390

For BC = 27: 27 = ABC / 15 ABC = 405

For BC = 28: 28 = ABC / 15 ABC = 420

For BC = 29: 29 = ABC / 15 ABC = 435

For BC = 30: 30 = ABC / 15 ABC = 450

For BC = 31: 31 = ABC / 15 ABC = 465

For BC = 32: 32 = ABC / 15 ABC = 480

For BC = 33: 33 = ABC / 15 ABC = 495

For BC = 34: 34 = ABC / 15 ABC = 510

For BC = 35: 35 = ABC / 15 ABC = 525

For BC = 36: 36 = ABC / 15 ABC = 540

For BC = 37: 37 = ABC / 15 ABC = 555

For BC = 38: 38 = ABC / 15 ABC = 570

For BC = 39: 39 = ABC / 15 ABC = 585

For BC = 40: 40 = ABC / 15 ABC = 600

For BC = 41: 41 = ABC / 15 ABC = 615

For BC = 42: 42 = ABC / 15 ABC = 630

For BC = 43: 43 = ABC / 15 ABC = 645

For BC = 44: 44 = ABC / 15 ABC = 660

For BC = 45: 45 = ABC / 15 ABC = 675

For BC = 46: 46 = ABC / 15 ABC = 690

For BC = 47: 47 = ABC / 15 ABC = 705

For BC = 48: 48 = ABC / 15 ABC = 720

For BC = 49: 49 = ABC / 15 ABC = 735

For BC = 50: 50 = ABC / 15 ABC = 750

For BC = 51: 51 = ABC / 15 ABC = 765

For BC = 52: 52 = ABC / 15 ABC = 780

For BC = 53: 53 = ABC / 15 ABC = 795

For BC = 54: 54 = ABC / 15 ABC = 810

For BC = 55: 55 = ABC / 15 ABC = 825

For BC = 56: 56 = ABC / 15 ABC = 840

For BC = 57: 57 = ABC / 15 ABC = 855

For BC = 58: 58 = ABC / 15 ABC = 870

For BC = 59: 59 = ABC / 15 ABC = 885

For BC = 60: 60 = ABC / 15 ABC = 900

For BC = 61: 61 = ABC / 15 ABC = 915

For BC = 62: 62 = ABC / 15 ABC =