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The sum of three numbers is 24. Twice the smallest number is 2 less than the largest number. The largest number is equal to the sum of the smallest and middle number. What are the three numbers?.

Respuesta :

linandrew41

Known information:

  • the sum of three numbers: 24
  • the smallest number is 2 less than the largest number
  • the largest number is equal to the sum of the smallest and middle number.

Let us set up some variables for our terms:

  • smallest number --> S
  • middle number --> M
  • largest number -- L

Let us set up some equations in terms of our known information

  • S + M + L = 24
  • S = L - 2
  • L = S + M

Let us set up everything in terms of L, because in the first equation, we will be able to get rid of all the other variables but L allowing us to solve the equation:

              (S + M) + L = 24 --->   L + L = 24

              2L = 24

              L = 12

Since L = 12, we know that S = L - 2:

              S = L - 2 = 12 - 2 = 10

Since now we know that L = 12, and S = 10, and L = S + M:

              L = S + M

              12 = 10 + M

               M = 2

So our answer is 2, 10, 12

Hope that helps!

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