AVERAGE OF PAYMENTS. TALK: While work in average of payments does not have a practical value for many pupils, any of them may have occasion to use it in later life. There is nothing difficult about it, and a few lessons in it may be helpful. Introduce the subject in this way: 1. The use of $3 for 2 mo. is equal to the use of $1 for how many months? The use of $3 for 2 mo. equals the use of $1 for 3 times 2 mo., or 6 mo. 2. The use of $4 for 1 mo. will balance the use of $2 for how many months? The use of $4 for 1 mo. will balance the use of $2 for 2 mo., because $2 is of $4. Hence, it must be used twice as long as $4. 3. $100 for 2 years will balance $50 for how long? $50 is of $100; hence, it must be used twice as long as the $100, or 4 yr. The average of payments is the way of finding the time at which two or more sums of money, due on different dates, may be paid so that neither debtor nor creditor lose by the transaction. This is sometimes called equation of payments. The average time, or equated date, is the day on which the whole sum owed may be paid without loss to either party. The term of credit is the time allowed on a debt item before it is due. PROBLEMS. PROBLEM: A merchant owes a wholesale house $300, due in 3 mo.; $150 due in 4 mo.; and $200 due in 6 mo. What is his average term of credit? EXPLANATION: $300 for 3 mo. = 3 × $300, or $900 for 1 mo. $150 for 4 mo. = 4 × $150, or $600 for 1 mo. $200 for 6 mo. = 6 x $200, or $1200 for 1 mo. $650 for the periods above = $2700 for 1 mo. The time of cr. on $2700 will be as many mo. as mo. 4 mo. 4 da. = NOTE.- Where the fraction of a day is more than, call it 1 day. PROBLEM: W. A. Clark bought of Browning, King & Co. these bills of goods: Jan. 10, $400 due in 60 da.; Feb. 10, $600 due in 90 da., and March 1, $300 due in 30 da. What is the average time of payment? EXPLANATION: = 1st bill is due Jan. 10+ 60 da. Mar. 11. 2d bill is due Feb. 10 + 90 da. = May 12. 3d bill is due Mar. 1+30 da. = Apr. 1. Assume that all are settled on May 12. Then, The first bill is over due May 12 for 62 days. A. H.-26 Then I owe the interest on $1 for 12600 da. The int. on $1300 is due for 13 of 12600 da., or 10 da. .. the average date is 10 da. before May 12, or May 2. PROBLEM: Wilhelmina Case bought a piano for $700 on 6 months credit. She paid $300 cash. In what time should the balance be paid! SOLUTION: $700 for 6 mo. = 6 x $700, or $4200 for 1 mo. The balance, or $400, should be paid in as many months as credit on $400 will equal $4200 for 1 mo. This is of 4200, or 101. .. the balance should be paid in 10 mo. REMARK: The preceding problems include all the phases of the subject ordinarily needed. The pupil who has gone over these carefully should be able to do intelligent work in averaging any set of payments. PART NINE. POWERS AND ROOTS. "The world generally gives its admiration not to the man who does what nobody else ever attempts to do, but to the man who does best what multitudes do well.” -Macaulay. MOTHER AND TEACHER. HEN mothers understand what true education is, and realize what a power for good every good teacher is in the life of a child, and set themselves to secure the one and to preserve the other, public opinion and school officials will be with them. Then we shall have schools that are homes where children live, each free to unfold himself, through his activities, and each teacher has leisure to study every pupil and to choose the methods which appeal to his temperament, and fit his intellectual gifts. But the first step in bringing the home and the school together must consist in the closer relations of mothers and teachers. It is strange, that, though allies in the most important work of the world, they only occasionally understand each other. The various associations of mothers and teachers should be of value in uniting them in meetings, under any name, which bring them close to one another in the genuine exchange of views and interchange of views about children. THE SUCCESS LIBRARY, Vol. II. |