1^6 ARITHMETIC. 



EXAMPLES. 



I. A owes B 190I. to be paid as follows, viz. 50I. in 6, 

 months, 60I. in 7 months, and Sol. in 10 months j what 

 is the equated time to pay the whole ^ 



50X 6 = 300 



60X 7 = 420 



80X10=800 



50 + ^0 + 80=190)1520(8 



1520 Ans. 8 months. 



2. A 



Althoiigh this rule be not accurately true, yet in most questions, 

 that occur in business, the frror is so trifling, that it will be much 

 used. 



That the rule is universally agreeable to the supposition may 

 ^iie thus demonstrated. 



f J = first debt payable, and the distance of its term of 

 I payment t. 



J^et ^ -O = last debt payable, and the distance of its term T, 

 I X = distance of the equated time. 

 (^ r = rate of interest of il. for one year. 



fThe distance of the time f and k 

 is = X — L 

 The distance of the time T and x 

 is = T—x. 



Now ttie interest of J for the time x — t is x — /X^'" > and the 

 interest of JD for the time T—x is T—xX-Dr ; therefore x — t 

 X^r = 7' — .Y >^ /)r by the supposition ; and frpm this equation^ 

 X is found =""2)+T' which is the rule. And t^e same might 

 be shewn of any number of payments. 



The true rule is given in equation of payments by decimak. 



