ALGEBRA 



195 



ALGERIA 



2x+ y z= 



(1) ......................... x+ y+ z=10 



(2) ......................... 3x+2H- 4^=33 



(3) ......................... 9z+3y 32=18 



(4) Bring down (2) .......... 3z+2j/+ 42=33 



(5) Multiply (1) by 3 ....... 3j+3j/+ 32=30 



(6) Subtract (5) from (4) ____ - y-f 2= 3 



(7) Multiply (2) by 3 ........ 9x+6y+ 122=99 



(8) Bring down (3) .......... 9j-+3y 32=18 



(9) Subtract (8) from (7).... 3j/+15z=81 

 (10) Multiply (6) by 3 ........ 3y+ 32= 9 



Add (9) and (10) ........ 182=90 



(12) Therefore ............... 2= 5 



(13) Substituting the value of 



z in (6) ................ y+5= 3 



(14) ....................... y=~2, or y= 2 



Substituting in (1) ....... x+2+5=10 



(16) ......................... j=10 7, or 3 



(17) Proof ................... 3+2+5=10 



Solve the following problems, testing in each 



instance the correctness of your work : 



x + 2y- *= 

 1. Solve 1 3x + 4-5z = 4 



2. Solve 



3. A merchant sold to a customer 8 yards of 

 silk and 4 yards of gingham for 18 dollars; at 

 the same rate he sold to another customer 5 

 yards of silk and 10 yards of gingham for 15 

 dollars. What was the price of each per yard? 



The conditions of this problem may be 

 stated algebraically as follows: 



Let x = number of dollars one yard of silk 



costs, 

 and i/ = number of dollars one yard of ging- 



ham costs. 

 n 8x+ 4j/ = 18 

 5ar+ 10y=15 



* 

 These equations are solved according to the 



rules that have been given in the preceding 

 paragraphs. 



4. Three numbers have the following relations : 

 three times the first plus the secnm! plus twice 



third equals 38; four times tin- lirst minus 

 the second plus thi muls 40; 



and the first plus three times the second minus 

 ird equals it are the numbers? 



Advanced Algebra. The basic principles of 



algebra have been covered in th. j.n c.-dnn: 



paragraphs, and if you have master* d the 



t nations therein given you will be able to 



take up more advanced work. The subjects of 



ions, factoring, highest common divisor 



and least common multiple can be ma*t 



by anyone who has an intelligent understand- 



in tr nf those subjects from the view-point of 



met ic. and from them the student may 



work through the subject of quadratic equa- 

 tions. 



The study of algebra can be made as absorb- 

 ing as that of astronomy or literature, and it 

 also offers exceptional opportunities for mental 

 discipline, since it can be mastered only with 

 persistent attention to detail and demands 

 accuracy and concentration in the highest de- 

 gree. B.M.W. 



Nearly all school-book publishing houses have 

 several good texts on algebra for beginners, spe- 

 cializing in these as well as In more advanced 

 text-books. Any such publisher (names can be 

 secured from teachers or county superintendent) 

 will be glad to give advice upon the subject. 



ALGER, ahl f jur or awl' jur, HORATIO (1834- 

 1899), an American author of books for boys, 

 whose Ragged Dick, Tattered Tom and Luck 

 and Pluck series have been sold by the hun- 

 dreds of thousands. As the names suggest, 

 they deal with penniless heroes who, by good- 

 ness, as well as "luck and pluck," reach suc- 

 cess. Alger was for a time a Unitarian 

 preacher, but becoming especially interested in 

 the lives of self-supporting boys gave up his 

 pastorate to help such boys, as well as to write 

 about and for them. 



ALGERIA, alje'ria, a country of about 

 343,500 square miles, in Northern Africa, with 

 650 miles of Mediterranean seacoast on the 

 north, and with Morocco and Tunis on the 

 west and east. It is nearly as large as the 

 combined states of Ohio, Indiana, Illinois, Wis- 

 consin and Michigan. The southern boundary 

 is indefinite and unimportant, merging into the 



DESERT OF SAHARA 



ALGERIA 



! finite southern boundary. 

 h iniliH-Mce pre- 

 vails throughout the region. 



inds of the great Sahara Desert. Tho 



\ has a population of over 5.230,000. It 



has belonged to France since 1830, but has 



always been a liability rather than an asset to 



