SOLUTION: Three no are in continued proportion .if mean proportional is 12 and sum of other two is 26 then find the no

Question 1099257: Three no are in continued proportion .if mean proportional is 12 and sum of other two is 26 then find the no
Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Three no are in continued proportion .if mean proportional is 12 and sum of other two is 26 then find the numbers
a/b = b/c
b=12
a/12=12/c
ac = 144
a =144/c
a+c =26
substitute a
144/c +c =26
multiply equation by c
144 +c^2 = 26c
c^2-26c+144=0
c^2-26c=-144
Add 169 to both sides
c^2-26c +169 =169- 144
(c-13)^2= 25

take the square rooton both sides
(c-13)=+ /- 5
either c-13 = 5 or c-13 = -5
c= 18 or c= 8
ac =144
a = 144/18 or 144/8
a= 8 or 18

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A formal mathematical solution as provided by the other tutor is fine; the student should understand how to solve the problem by that method.

However, if a formal mathematical solution is not required, the problem is easily solved mentally if the student understands the given information.

The given information tells us that we are looking for two numbers whose sum is 26 and whose product is 12^2=144.

144 = 12*12; sum is 12+12=24
144 = 16*9; sum is 16+9=25
144 = 18*8; sum is 18+8=26

ANSWER: the numbers are 8, 12, and 18

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