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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?​

Respuesta :

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.

batolisis

The minimum number of letters that John will have to send to ensure Peter receives his letter is : 127 letters

Applying the given information;

size of house number = Four digits which is a multiple of 5 and 7

House number ends with 0

given that the last number has a 0 digit the house number is divisible by 5 because it is divisible by 10

The Four digit house number will fall between : 1000 to 9999

  1. Determine the total numbers that are divisible by 7 and 10

    ( 1000 / 70 ) = [tex](14 + 2/7) - 2/7)*70 + 70 = 1050[/tex]

    ( 9999 / 70 ) = [tex]( 142 + 59/70)- 59/70)*70= 9940[/tex]

∴ The minimum number of letters of a four digit number that is a multiple of    5 and 7 and whose last digit = 0 will be

     142 - ( 14 + 1 ) = 127 letters

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