+0  
 
0
57
1
avatar

Four distinct integers $a$, $b$, $c$ and $d$ have the property that when added in pairs, the sums 10, 18, 19, 20, 21, and 29 are obtained. What are the four integers in increasing order? (place a comma and then a space between each integer)

 Jan 26, 2021
 #1
avatar+116126 
+1

Let   the integers in increasing order be  a, b, c, d 

 

All we know  for sure is that

 

a + b =   10

a + c  =  18

b + d  =  21 

c + d =   29

 

Subtracting the    first equation  from the second  we  have that     c - b =  8    ⇒  c =  8 + b

 

Either    a +  d   = 19    or b +  c  = 19

Let's assume the  second  is true

Then  2b + 8   =  19          but b isn't an integer  here

 

So

a +d    = 19

And

b + c =  20

 

So

 

b + 8 + b =  20

2b + 8 = 20

2b =12

b = 6

 

a  = 4

 

c=  14

 

d = 15

 

So

 

a   b    c    d    

4   6   14  15

 

 

cool cool cool

 Jan 26, 2021
edited by CPhill  Jan 26, 2021

59 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar