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34^ ALGEBRA. 



■ First, the given equations, cleared of fractions> become 



I2.V-f- Oj-\- 62 ~z 1 40 3 



2cAr-|- 1 5y--{- 1 2s n: 2 S 20 



3 c,v-|-24v-f- 202 11: 45 60 

 Then, if the secorid of these equations be subtracted 

 from double the first, and three times the third from five 

 times the second, v/e shall have 



4;c-[- J— 156 

 io;<-j-3v^^42o 

 And again, if the second of these be subtracted from 

 three times the first, it will give 



1 2X — I c.v=465 — 4 2 o, or x zz '^y =z 24 ; 

 Therefore jzrz It; 6 — 4X=z6y 



1488— 8r— i2;c 



And 2= '■ zri2o. 







3. Given x-\-y^z-=zi,ii x-\-y — 211:25, ^^"^^^ AT-*—)' — r 

 mp *, to find K, y and 2. Ans. xzii:2o, jzzzS and2iizz3» 



4. Given x-^-yZZiay ^-}-2Zr:^, and ^y-j-szz^ ; to find x^ 

 y and z. 



5. Given < .7.Y-[-f)-|-y2;=:;/ > ; to find AT, )? and z* 



-^ Cgllec'Tion of ^UESTIONSy producing Sim* 



FLE E.^UATIOyS, 



I. To find two such numbers, that their sum shall be 

 40, and their difference 16. 



Let A? denote the less of the two numbers requirsd. 

 Then will x-^j6= the greater, 

 And ;)f-j^.v-^ 1 6=1=40 by the question ; 

 That is, 2.vnz40 — 16^2:24, 

 Or X:=:'y zzzizzz less nutober, 

 And .\'-J-i6z:=:i2-^i6zi2oz=z greater number required. 



2. What 



