Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.