We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
40
3
avatar

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
avatar
+1

3 + 5  +  7= 15

 

3 x 5 x 7  =105

 

105 / 15  = 7  and 5 is the answer.

 Nov 6, 2019
 #2
avatar+19773 
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+105411 
+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

6 Online Users

avatar