Answer:
The minimum number of letters John has to send to be sure that Peter receives his letter is 127 letters
Step-by-step explanation:
The four digit numbers that are multiples of 5 and 7 with the last digit = 0 is found as follows
Since the last digit of the house number = 10, then the house number is divisible by 10 which also meets the condition that the house number is divisible by 5
We have the four digit numbers from 1000 to 9999
Hence the numbers divisible by both 7 and 10 are from (1000/70 (Which is 14 + 2/7) - 2/7)×70 + 70 = 1050 to (9999/70 (Which is 142 + 59/70)- 59/70)×70= 9940
Which gives 142 - 15 = 127 numbers which are four digit number multiples of 5 and 7 with the last digit = 0
Hence the minimum number of letters John has to send to be sure that Peter receives his letter = 127 letters.
