John wants to send a letter to Peter, who lives on Tesla

Street. John doesn't remember the house number.

However, he knows that it has 4 digits, it is a multiple of 5

and 7 and that the last digit is 0. What is the minimum number

of letters that John has to send to be sure that Peter receives his letter?

Question

Keegan Hansen

Mathematics

16 May, 17:46

John wants to send a letter to Peter, who lives on Tesla

Street. John doesn't remember the house number.

However, he knows that it has 4 digits, it is a multiple of 5

and 7 and that the last digit is 0. What is the minimum number

of letters that John has to send to be sure that Peter receives his letter?

+2

Answers (1)

Know the Answer?

Doogie · Answer 1

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.