Answered

Connect with a community that values knowledge and expertise on IDNLearn.com. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

how many 4 digit numbers n have the property that the 3 digit number obtained by removing the leftmost digit is one ninth of n

Sagot :

Sqdancefanidn

Answer:

  7

Step-by-step explanation:

We want to find the number 4-digit of positive integers n such that removing the thousands digit divides the number by 9.

__

Let the thousands digit be 'd'. Then we want to find the integer solutions to ...

  n -1000d = n/9

  n -n/9 = 1000d . . . . . . add 1000d -n/9

  8n = 9000d . . . . . . . . multiply by 9

  n = 1125d . . . . . . . . . divide by 8

The values of d that will give a suitable 4-digit value of n are 1 through 7.

When d=8, n is 9000. Removing the 9 gives 0, not 1000.

When d=9, n is 10125, not a 4-digit number.

There are 7 4-digit numbers such that removing the thousands digit gives 1/9 of the number.

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.