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According to the Encyclopaedia Britannica, Thales of Miletus lived from 
640 B. C. to 546 B. C; and on May 28, 585 B. C. occurred the total eclipse of 
the sun, which he had predicted. many years before its occurrence. 



ARITHMETIC. 



Conducted by B. F. FTHKEL, Springfield, Mo. All contributions to this department should be sent to him. 



SOLUTIONS OF PROBLEMS. 

52. Proposed by F. P. MATZ, So. D., Ph. D., Professor oi Mathematics and Astronomy in Irving College, 
Mechanicsburg, Pennsylvania. 

Py selling a horse for ,ff=$150 cash, I gain p=20 per cent. At what price should I 
sell the horse and wait d=90 days, money worth m=6 per cent., in order to gain 9=25 per 
cent.? 

Solution by the PROPOSER. 

Obviously the cost of the horse is C=Tl / ( 1 +~) 1 of $il,=$125 ; 

and, consequently, the selling price, in order to gain q per cent., must be 

P> = ( 1 +-^) of $C,=$156.25, which must be divided by the proceeds of $1 for 

d days at m per cent.; that is, the required result becomes 

P = (100_±gy 36000 W |=$158 .62944. 
U00+pA36000-dm/ ' 

Also solved by H. C. WILKES. 

68. Proposed by P. S. BEEG, Larimore, North Dakota. 

$500. Wooster, Ohio, September 2nd, 1886. 

One year after date we, or either of us, promise to pay to the order of J. M. W. Five 
Hundred Dollars for value received with interest at 7 per cent, from date. 

J. C. 
M. C. 
Endorsed, May 13, 1893, $75.00. 

" September 1, 1894, $300.00. 

What was due April 1st, 1895 ? 

Solution by H. C. WILKES, Skull Bun, Virginia. 

As the first payment $75 is less than the interest then due, compute the 
interest to the time of the second payment.