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?
Given:
a+b=c .... Eq 1
a+c=d .... Eq 2
b=c+d .... Eq 3
{ d ε Z | d > 0 }
Maximum value of a = ?
Sub Eq 3 into Eq 1:
a + (c + d) = c
a = - d .... Eq 4
At this point, ask yourself "what value of d (remembering that d is a positive integer) will yield the largest possible value of a?".
This is not the way
I need a numerical value for a
If I see that then I will say
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To find the greatest value of a, we need to examine the given equations and see if we can derive any useful information.
Let's start with the equation a+b=c. Since b=c+d, we can substitute b with c+d in the first equation:
a + (c+d) = c
Simplifying this, we get:
a + d = 0
Now let's look at the second equation, a+c=d:
a + c = d
If we combine this with the previous equation, a+d=0, we can solve for a:
a = d - c
Since d is a positive integer, the greatest value of a would occur when c is at its minimum, which is 1. In that case:
a = d - 1
Therefore, the greatest value of a is d - 1.