SIMPLE EQIJATI0N3. 347 



2. What number is that, whase j part exceeds its -^ 

 part by 16 ? ' , 



Let X equal number required^ 



Then will its 4 P^rt be — , and its 4 part — $ 

 ^3 ^ 4 



a: a; 

 And therefore zzii6 by the question, 



3 4 



That is,*Y — '^2-485 or ^x-- — 3A'ZI 192 ; 

 4 

 "V/hcnce a\::z: 192 the number required. 



3. Divide 10001 between A, B and C, so that A shall 

 Jjave 72I. more than B, and C lool. more than A. 



Let A:m' 3 bhnre of the given sum. 

 Then will a;-}-72z:;A's sliare, 

 And a;-j- i , iZzC's share, 

 And the sum of all their shares ^-}-Ar-F|-72-|-Ar-j^i72, 



Or 3^-{-244ZZiooo by the question ; 

 That is, 3A,'= 1 000-— 244=756, 



Or xzz'-^=2S2\. == B's share, 



And ;v-J-72=252+72Zr324l. = A's share. 



And ;v-f- 1 7211:25 2+ 1 72=424). :;==: C's share. 



25 2I. 



324I. 



424I 



I cool, the proof. 



4. A prize of loool. is to be divided between two per- 

 sons, whose shares therein are in the proportion of 7 to 

 9 ; required the share of each. 



Let *r equal first person^s share, 

 Then will 1000 — <«^equal second person's share, 

 And X I looQ — .V :: 7 : 9, by the question. 



That 



