SOLUTION: I cannot seem to find how to resolve this question. I made average pies, tried adding equations. I do not know what to do next! Thanks for your help. The average between a and

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Question 1006157: I cannot seem to find how to resolve this question.
I made average pies, tried adding equations. I do not know what to do next! Thanks for your help.
The average between a and b is 9, between b and c is 6, between c and d is 15. What is the average between d and a?
Thank you so very much!
Caroline
Found 3 solutions by josmiceli, Theo, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Using definition of average:
(1)
(2)
(3)
---------------------
Multiply both sides by
(1)
(2)
(3)
------------------
Subtract (2) from (1)
(1)
(2)
------------------

Add (3) to this result


--------------

Now, to get the definition of
an average, divide both sides by

The average of a and d is
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
(a + b)/2 = 9
(b + c)/2 = 6
(C + D)/2 = 15

from this you get:

a + b = 18
b + c = 12
c + d = 30

solve for b in a + b = 18 to get b = 18 - a

solve for c in b + c = 12 to get c = 12 - b

start with c + d = 30

replace c with 12 - b to get:

12 - b + d = 30

replace b with 18 - a to get:

12 - (18 - a) + d = 30

simplify to get:

12 - 18 + a + d = 30

combine like terms to get -6 + a + d = 30

add 6 to both sides of this equation to get:

a + d = 36

divide both sides of this equation by 2 and you get:

(a + d)/2 = 18

the average of a + d is equal to 18.

i believe that's the answer you are looking for.


Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

I cannot seem to find how to resolve this question.
I made average pies, tried adding equations. I do not know what to do next! Thanks for your help.
The average between a and b is 9, between b and c is 6, between c and d is 15. What is the average between d and a?
Thank you so very much!
Caroline
If 9 is the average of a and b, then sum of a and b is 2(9), or 18, so a + b = 18______b = 18 - a ------- eq (i)

If 6 is the average of b and c, then sum of b and c is 2(6), or 12, so b + c = 12 -------- eq (ii)

If 15 is the average of c and d, then sum of c and d is 2(15), or 30, so c + d = 30 ------ eq (iii)

18 – a + c = 12 ------- Substituting 18 – a for b in eq (ii)

c = a – 18 + 12

c = a – 6 -------- eq (iv)

a – 6 + d = 30 ------- Substituting a - 6 for c in eq (iii)

a + d = 30 + 6

a + d = 36

Average of a + d: , or , or  

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