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Given that a+b=c, a+c=d and b=c+d, where d is a positive integer, what is the greatest value of a?

Guest Nov 14, 2018
 #1
avatar+92785 
+1

a + b  = c       ⇒    b  = c - a    (1)

a + c  = d

c + d  = b    (3)

 

Equating  (1) and (3)

 

c + d  =  c - a

d  = - a

 

So

 

a  =  -d

 

 

 

cool cool cool

CPhill  Nov 14, 2018
 #2
avatar
0

is -d the largest value of a

Guest Nov 14, 2018
 #3
avatar+92785 
+1

We can prove this

 

a + c  = d

-d + c  = d

c = 2d

 

And

c + d  = b

2d + d = b

3d = b

 

So....using the original equations with the substitutions...

 

a + b  =  c  ⇒   -d + 3d =  2d

a + c  = d ⇒  -d + 2d  =  d 

c + d  = b  ⇒  2d + d  = 3d

 

 

 

cool cool cool

CPhill  Nov 14, 2018
 #4
avatar
0

would you be able to find the greatest numerical value of a? 

1)-3

2)2

3)-2

4)1

5)-1

Guest Nov 14, 2018
 #5
avatar+92785 
0

We don't know the numerical value of "a"......it would depend upon the value of "d"

 

 

cool cool cool

CPhill  Nov 15, 2018

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