+0  
 
+1
100
3
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The sum of three consecutive one-digit, positive, odd integers is one-seventh of the product of the same three integers. What is the middle integer when the three integers are listed in ascending order?

 Nov 6, 2019
 #1
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+1

3 + 5  +  7= 15

 

3 x 5 x 7  =105

 

105 / 15  = 7  and 5 is the answer.

 Nov 6, 2019
 #2
avatar+22114 
0

[(x-2) + (x) + (x+2)  ]  =  1/7(x-2)(x)(x+2)

3x   = x^3-4x

21 = x^2-4

0 =x^2 -25    x = -5 (throw out) or 5

 

so the numbers are   5-2 = 3   5   and 5+2 = 7         (as guest posted)

 Nov 6, 2019
 #3
avatar+109740 
+1

Let the smallest integer   be N - 2

Let the   middle integer be N

Let the largest integer  be  N + 2

 

So  the sum of these  =   3N

 

So we have that

 

3N (7)   = (N + 2) (N - 2) N

 

21N  = (N^2 - 4)N

 

21N  = N^3 - 4N       rearrange as

 

N^3 - 25N = 0       factor

 

N (N^2 - 25)  = 0

 

N ( N + 5) (N - 5)  =  0

 

Setting each factor to 0  and solving for N   produces  N  = 0  ,  N  =  -5   and n  = 5

 

So....the middle integer is  5

 

 

cool cool cool

 Nov 6, 2019

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