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Answer to Q173
From the picture above, if A + B = 8 (horizontally) and A + C = 13. Using other information that can be deducted from the picture, what is the value for A, B, C and D?
A + B = 8 (eqn i)
C - D = 6 (eqn ii)
A + C = 13 (eqn iii)
B + D = 8 (eqn iv)
From eqn i:
B = 8 - A (eqn v)
From eqn iii:
A = 13 - C (eqn vi)
Put eqn vi into eqn v:
B = 8 - 13 + C
B = -5 + C
B = C - 5 (eqn vii)
From eqn ii:
C = 6 + D (eqn viii)
Put eqn viii into eqn vii:
B = 6 + D - 5
B = 6 - 5 + D
B = 1 + D (eqn ix)
From eqn iv:
D = 8 - B (eqn x)
Put eqn x into ix:
B = 1 + 8 - B
B + B = 1 + 8
2B = 9
B = 9 ÷ 2
B = 4.5
From eqn x:
D = 8 - 4.5
D = 3.5
From eqn viii:
C = 6 + 3.5
C = 9.5
From eqn vi:
A = 13 - 9.5
A = 3.5
Answer: A = 3.5, B = 4.5, C = 9.5, D = 3.5
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