In △ABC, points X,Y and Z are on sides CB,AC and AB, respectively, so that cevians AX, BY and CZ are concurrent at P. If AY:YC=9:8,AZ:ZB=3:4, and ∣△CPX∣=112, determine, with justification, the area of △ABC and the area of △BZX. Relevent information: Theorem (48.5: Ceva's Theorem) In △ABC, cevians AX,BY, and CZ are drawn. Then AX,BY, and CZ are concurrent if and only if XC
BX + YA
CY + ZB
AZ
​
=1 Theorem (45) In △ABC, if D is on BC, then ∣△ACD∣
∣△ABD∣
​
= DC
BD
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. Theorem (49) If a,b,c, and d are real numbers with b

=0,d

=0,b

=d, and b
a
​
= d
c
​
, then ba= dc
​
b−d=a−c
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. Theorem (50) In △ABC, if cevians AX,BY, and CZ are concurrent at P, then XC
BX
​
= ∣△APC∣
∣△APB∣
​
. ∣△ABC∣ is notatiun used for area
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