Sorry I'm getting really confused here!
Here is the full detail of how I've attempted to solve it:
g=50
h=100
i=70
j=15
Which gives:
1) d = a - (b /2)
2) e = d + b
3) f = p - (c /2)
4) 50 = f - (d /2)
5) 100 = 50 + d
6) 70 = f - (e /2) + c
7) 15 = 70 + e
First I solve e by using 7):
15 = 70 + e
70 + e = 15
(-70 both sides)
e = -55
Which means that e = j-i
Now solve d using equation 5):
100 = 50 + d
50 + d = 100
(-50 from both sides)
d = 50
Which means that d = h-g
Now I solve f using equation 4):
50 = f - (d /2)
f - (d /2) = 50
Sub d since we know it
f - (50 /2) = 50
f - 25 = 50
(add 25 to both sides)
f = 75
which means that f = g + (d/2)
Now solve c using equation 6):
70 = f - (e /2) + c
f - (e /2) + c = 70
Sub f as we know its value
75 - (e /2) + c = 70
Sub e as we know its value
75 - (-55 /2) + c = 70
102.5 + c = 70
(-102.5 from both sides)
c = -32.5
Which means c = f -( e/2)
Now solve P using equation 3):
f = p - (c /2)
Sub f
75 = p - (c /2)
Sub c
75 = p - (-32.5 /2)
75 = p - (-16.25)
(Add 16.25 to both sides)
91.25 = p or
p = 91.25
You haven't considered the order of operations. Multiplication should be done before addition. So -16.25 should be multiplied by -1 before adding whatever necessary to subject p.
75 = p - (-16.25)
75=p+16.25
75-16.25=p
p=58.75
Which means p = f + (c/2)
Now solve b using equation 2):
e = d + b
Sub e
-55 = d + b
Sub d
-55 = 50 + b
(-50 from both sides)
-105 = b or
b = -105
Which means b = e-d
Finally solve a using equation 1):
d = a - (b /2)
Sub d
50 = a - (b /2)
Sub b
50 = a - (-105 /2)
50 = a - (-52.5)
(+52.5 to both sides)
102.5 = a or
a = 102.5 Again the same mistake as earlier. I hope you can correct it now.
Which means a = d + (b/2)
So:
a=102.5 (wrong somehow..)
b=-105
c=-32.5
d=50
e=-55
f=75
p=91.25 (wrong somehow..)
Testing gives:
1) 50 = 102.5 - (-105 /2) (wrong because 155)
2) -55 = 50 + -105 (ok)
3) 75 = 91.25 - (-32.5 /2) (wrong because 107.5)
4) 50 = 75 - (50 /2) (ok)
5) 100 = 50 + 50 (ok)
6) 70 = 75 - (-55 /2) + -32.5 (ok)
7) 15 = 70 + -55 (ok)
So I can see I've still managed to get the values of a and p wrong?