Ask Question
16 August, 19:49

Three numbers have an average of 14. The smallest number is six less than the middle number and the largest number is four less than twice the middle number. Use an algebraic model to find all three numbers.

+4
Answers (1)
  1. 16 August, 21:44
    0
    Let x (largest), y (middle) and z (smallest) be the 3 numbers.

    According to your question: z=y-3 and * = 2y-4

    Because we know the average we'd do the following: (x+y+z) / 3=14 (add all the three numbers and divide them by 3)

    Now just substitute

    [ (2y-4) + y + (y-3) ]/3=14

    Now simplify

    2y+y+y=4y

    -4-3=-7

    You get [4y-7]/3=14

    Now multiply both sides by 3

    4y-7=42

    Now add 7 to both sides

    4y=49

    Now divide both sides by 4

    y=49/4 (middle number)

    Substitute y in z and x

    z = (49/4) - 3 = 37/4 (smallest)

    x=2 (49/4) - 4 = 41/2 (largest)

    Those are the three numbers

    To check your work substitute x, y and z in the first equation, you will get 14
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Three numbers have an average of 14. The smallest number is six less than the middle number and the largest number is four less than twice ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers