and 75 А B R M rectangles. } of 7950=3975, area 4800, for it is the difference of the of one of the equal rectangles, as squares of the two numbers. ReA E Q R; and since E Q equals moving part K from the figure, 53, A E=3975-53, or 75; and A there would remain two equal B=75+53=128. squares, S QGE and CBM O, The required numbers are 128 and the two equal rectangles, O MD N and ACOR, whose comPROBLEM II. bined area is equal to 14400-4800, The sum of two numbers is 120, or 9600. It will now be evident and the difference of their squares that one of these small squares and is 4800; what are the numbers? one of the rectangles, as CB MO and O M D N, will form a rectSolution. angle whose area will be equal to 1 of 9600, or 4800, and whose side B D is 120. Then, C B=4800; 120, or 40, the smaller number; and A C=12040=80, the larger number. The required numbers are 80 and 40. PROBLEM III. breadth as 5 is to 3, and its area is 2 135 square rods; find length and breadth. Solution. Let A C represent the greater of the two numbers, and C B, in the Q same straight line, represent the smaller. Complete the square A B D E, and its area will be equal to 120o=14400. The square RON E is the square of the greater of the two numbers in question, and square C B M O is the square of Let A B be the length of the the smaller number. rectangle and A D its breadth, and On the square RON E, lay off complete the figure. Divide A B the square S QGE, equal to the into five equal spaces, and A D square CBM O; then will the part into three spaces each equal to one marked (K) be equal, in area, to of the spaces of line, A B. At these K E N A a B D с (Cer :) points of division draw lines par- 120%=selling price of one. allel to the sides and ends of the 80%=selling price of other. rectangle, thus dividing it into fif- The certain sum=120%=cost of teen small squares, as Q. Hence, one. 15 Q=135 square rods. The certain sum:80%=cost of Q=1-15 of 135=9 sq. rods, and other. Aa=V9=3 rods; then Certain sum certain sum + A B=5X3=15 rods, and 120% 80% A D=3X3=9 rods. price of both. 15 rods=length of rectangle, and Certain sum , certain sum + 9 rods=breadth. 1.20 .80 2(certain sum)=2 cts. or loss. ANSWERS TO QUESTIONS. 2(certain sum)+3(certain sum)[The following solutions to prob- 4.8(certain sum)=4.8 cents. lems published at the request of a .2(certain sum=1.8 cts. subscriber in November, are the Certain sum = 24 cts.= selling first to reach us. We are also in price each. receipt of solutions by B. F. Fin 120%=24 cts. kel, C. L. Martzolff and Anson McKinney, which we 1%=.2 cts. are compelled to omit for want of space. 100%=20 cts.=cost of one. • It is not our purpose to go 80%=24 cts. into the "Notes and Queries Busi- 1%=.3 cts. ness” to any great extent, because 100%=30 cts.=cost of other. we believe that there is something better for teachers than poring SOLUTION To Query 2. over the conundrums and their an By F. P. Geiger. swers, which are so often found under the head of “Notes and A perch=243 cu. ft. Queries” in some of the school 7773 perches = 19,2477 cu. ft.= journals of the day. If we can, given volume of arch-way. however, at any time, help a sub- 38,4914 cu. ft.=twice given volscriber who is honestly seeking ume of arch-way. light on some difficult point which (Width street)? X.7854 X 40 ft.comes up in his work as a teacher, twice volume of arch-way. we shall be glad to give a small amount of space for that purpose. (Width street)? X.7854 X 40 ft.= -Ed.] 38,4941 cu. ft. 31,416 ( width street)? = 38,494 SOLUTION TO Query 1. By F. P. Geiger. 38,494.5 A certain sum=selling price each (Width street) 31,416 knife. 1225.3+ cu. ft. 2 (certain sum) = selling price Width street =V 1225.3+ = 35+ both. ft. cu. ft. SOLUTION TO QUERY 1. 25% — 163%= 84%, the whole By J. F. Fairchild. loss. 100%= selling price of each $.02% = whole loss. knife - (A). 81% = $.02. . 100% = cost of first knife. 1 1% of $.02 = $.0024. 20%=gain of first. 84 100% + 20% = 120%, selling 83}%=834 times $.0024=$.20, price of first. cost of first. 120% = 100% - (A). 125% = 125 times $.0024 = $.30, 1% = 1ło of 100% = %. cost of second. 100% = 100 times %= 833%, cost of the first. 100% - 834% = 163%, gain on SOLUTION TO QUERY 2. first. By J. T. Fairchild. 100% = cost of the second knife. 7773 X 2 1555 cu. ft., the 20%= loss. volume of the cylinder, that is 40 100% - 20% = 80%, selling ft. long. Now to find the diameter price of second. of the cylinder, which is the width 80% = 100% ---(A). of the street, solve the rule back1% = 0 of 100% = 17%. ward for finding the volume. 100% = 100 times 11%= 125%, .. 1555 cu. ft. = 40 = 962,625 cost of second. sq. ft., the area of the base. 125% — 100%= 25%, loss on V (962,625 = 7854) = 35 ft., the second. width of the street. 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Y We must not forget that the next meeting of the Department of Superintendence of the N.E. A. will be held in Columbus. Four years ago the meeting was held in Cleveland, and it is generally admitted by those who attend the sessions of this department regularly that the Cleveland meeting has never been excelled in attendance and interest. We have a reputation to sustain, and we feel sure that Ohio teachers and superintendents will unite in making the coming meet ence com ing a great success. Supt. Shawan teachers recognize the fact that it with his excellent corps of teachers is not the only important one. The and enterprising board of educa- influence of the personality of the tion is already working hard to teacher, the surroundings in the perfect all the arrangements, and home life of the child, the comColumbus will do her best to make panionship of playmates, the neevery one welcome. President E. cessity of being prompt and puncH. Mark, of Louisville, an Ohio tual, and hundreds of other influboy, has already done considerable ences coming into the daily life and work on the program, and assures experience of the school are all us that a rich treat of good things powerful factors in the education will be served to all who attend. of the boys and girls. In recent We quote the following paragraphs years special attention has been from a recent letter written by him paid in many schools to the influto the editor: of beautiful surroundings “I have secured the following upon the children, and as a result persons for places on the program: neatly kept lawns, magnificent Mendenhall, Maxwell, Soldan, shade trees, and bright flowers are Goss, Prettyman of Baltimore, Martin of Boston, Steele of Gales each year becoming more burg, and have the promise of one mon on the school grounds of the or two others. State. In many instances beauti"I have concluded that Round ful pictures adorn the walls of the Tables add something to the inter school-room, and everything that est of the meeting and shall provide for meetings of the Round the mind of a thinking teacher can Tables in the afternoon.” suggest or her willing hand can The meeting will be held in Feb- perform, is done to make the ruary-probably February 22-24 school-room a home for the chiland we hope to be able to publish dren. It is impossible to overestithe exact dates, together with the mate the value of such influences in general program and arrange the management of the school, and ments, in the January MONTHLY. in the development of character. In the meantime, let as many teach When one considers the condition ers and superintendents as possible of many of the school-rooms in make their arrangements to attend which he was compelled to stay this great educational convention, when a boy, and contrasts that conwhich stands for so much in the dition with the home-like atmoseducational progress of the day. phere in which many of the chil dren of to-day are permitted to live, WHILE the text-book will al- he feels like exclaiming, ways remain an important factor in "Backward, turn backward, 0, the work of education, yet all true time, in your flight; |