364 ALGEBRA. 



Let »V = pounds the cloth cost, 

 Then 2^. — .v =^ the whole gain ; 

 But 100 : a; : : .V : 24 — x by the question. 



Or ;tf* rr IOC v,<24 — xzz 2400— iooat ; 

 That is, »v*-|-iooJV= 2400 y 

 Whenct^ a; *-|-iQo;f-|~ 2500 =2400-1-250011:4900 by com- 

 pleting the square, 



And x~\-^ozz ^4()oo.z:z 70 by extracting the roots. 

 Consequently, a*= 70— 5 := 20:::;: price of the cloth. 



5. A person bought a number of oxen for Sol. and if 

 he had bought 4 more for the same money, he would have 

 paid il. less for each 5 how many did he buy ? 



Suppose he bought ^ oxen. 



So 

 Then — = price of each, 



And —7— =; price of e^ich, if Ar+4 Had cost 80U 

 80 80 



But —r= -— - *|-i by the question, 



X ^"y"4 



Sox 

 Or 80;;=: — , l-x, 



Or 80^+320 rr8o^4"^*+4^> 

 That is, x"" +4x1:^320 *, 



Whence iv* 4-4a;-|- 4^:320-1- 4=1: 3 24 by completing the 

 square ; 



And Ar-}"«<^^^\/324=i8 by evolution ; 

 Consequently ;czzi8 — >2=:i6 =: number of oxen re- 

 quired. . 



6. What two numbers are those, whose sum, product 

 and difference of . their squares are all equal to each other ? 



Let X r= greater number, 

 And y zz less j 



Then 



