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qwelly [4]
2 years ago
9

Five double-digit numbers We have five consecutive positive double-digit integers. If we swap places on the numbers in the large

st number, the sum of the five numbers increases by 1 more than the mean of the original numbers. What is the lowest number?
Mathematics
1 answer:
barxatty [35]2 years ago
3 0

Answer:

  • 33

Step-by-step explanation:

<u>Let the numbers are:</u>

  • 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

<u>We are looking for the number x + 4 = ab such that:</u>

  • 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

<u>By trial method we get the solution:</u>

  • a = 3, b = 7

<u>Since x + 4 = 37, the lowest number is:</u>

  • x = 37 - 4 = 33

<u>Lets verify:</u>

  • 33, 34, 35, 36, 37

<u>The sum is:</u>

  • 5*33 + 10 = 175

<u>The mean is:</u>

  • 35

<u>Change the largest number tp 73 and find the sum again:</u>

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

The sum has increased by 1 more than 35

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