Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Five double-digit numbers We have five consecutive positive double-digit integers. If we swap places on the numbers in the largest number, the sum of the five numbers increases by 1 more than the mean of the original numbers. What is the lowest number?

Sagot :

mhanifa

Answer:

  • 33

Step-by-step explanation:

Let the numbers are:

  • x, x + 1, x + 2, x + 3 and x + 4
  • Their sum is 5x + 10
  • Their mean is (5x + 10)/2 = x + 2

If we swap the digits on the largest number, the sum increases by 1 more than x + 2

We are looking for the number x + 4 = ab such that:

  • ba - ab = ab - 2 + 1
  • ba = 2ab - 1
  • 10b + a = 2(10a + b) - 1
  • 10b + a = 20a + 2b - 1
  • 8b = 19a - 1
  • 19a = 8b + 1

By trial method we get the solution:

  • a = 3, b = 7

Since x + 4 = 37, the lowest number is:

  • x = 37 - 4 = 33

Lets verify:

  • 33, 34, 35, 36, 37

The sum is:

  • 5*33 + 10 = 175

The mean is:

  • 35

Change the largest number tp 73 and find the sum again:

  • 175 + (73 - 37) = 175 + 36 = 175 + 35 + 1

The sum has increased by 1 more than 35

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.