SIMPLE Ec^JATIONS. 349 



7. Out of a cask cf wine, \vhich had leaked away y, 

 21 gallons were drawn ; and then, being gauged, it ap- 

 peared to be half full : how much did it hold ? 



Let it be supposed to have held x gallons, 



Then it v/ould have Jeaked — gallons, 



3 



And consequently there had been taken away 2ir-j gal. 



.V X 



But 21-f-— =r — , by the (question;. 



That is, 63+;cr=::^, 



Or i26-\-2x—i,x ; 

 Hence 3a;-^2a;= 126, 

 Or ;v := 126 :i= number of gallons required. 



8. What fraction is that, to the numerator of which if 

 I be added, the value will be y ; but if i be added to the 



4enominator, its value will be ^ ? 



X 



Let the *fraction be represented by — , 



y 



X-\-l __ ^ 



Then will 



y ^'' 



Or 3Af-f-3 —J, 



And 4^:zzj5-j-i, 

 Hence 4.V — 3^ — 3-3;-}- 1— -y, 

 That is, a: — 3= i. 



Or A?=r4, and ;=3x4.3z= 124-3=^55 

 So that -j^ ^zz fraction required. 



9. A market woman bought a certain number of eggs,^ 

 at 2 a penny, and as many at three a penny, and sold them™ 

 all again at the rate of 5 for 2d. and, by so doing, lost 4d. 

 What number of eggs hacf she ? 



Let 



