164. A owned two farms for the better of which he asked 50% more than for the other. Not finding a purchaser, he reduced the price of the better 331%, and the price of the other 20%, and sold them both for $5580. What was the price asked for each?

165. A merchant bought a bill of goods amounting to $3257 on a credit of 3 months, but was offered a discount of 21% for cash. How much would he have gained by paying cash, money being worth 7%?

166. Which is better for me, to buy 6% bonds at 72%, or to invest my money in mortgages bearing 8%? How much better is it?

167. A machine shop was insured at an annual rate of 3%, the premium paid being $750. For how much was it insured?

168. A merchant bought broadcloth at a discount of 25% from the marked price, receiving besides a discount of 5% for cash. If he sold it at an advance of 10% on the marked price, what was his gain per cent?

169. A commission merchant received 35,000 bushels of oats, which he sold at 32 cents per bushel. He was instructed to invest the proceeds, together with $4000 cash sent him, in prints at 5 cents per yard. If his commission both for buying and for selling was 2%, how many yards

of prints did he buy?

170. I find that I owe A 50% more than I owe C, and B 331% more than I owe A. Now if I owe B $800 more than I do C, how much is my indebtedness to each?

171. A man at his marriage agreed that if at his death he should leave only a daughter, his wife should have of his estate; and if he should leave only a son, she should have. He left a son and a daughter. What fractional part of the estate should each receive, and how much was each one's portion, if the estate was worth $6591 ?

172. How many shares of stock, at 1134, can a broker purchase for me with $22,675, brokerage %?

173. I am offered 6% stock at 84, and 5% stock at 72. Which investment is preferable, and how much?

174. I am desirous of securing an income of 61% or 7% on my investments. Can I do it by purchasing 5% stock at 75%? What will be the rate of income?

175. I have, as the net proceeds of a consignment of goods sold by me, $3816.48, which the consignor desires me to remit by draft at 2 months. If the rates of exchange are 3% premium, and the rate of interest 6%, what will be the face of the draft?

176. A man bought a horse and a carriage, paying twice as much for the horse as for the carriage. He sold them both for $662, receiving 15% more for the horse, and 8% more for the carriage than they cost him. What did they each cost him?

177. A man sold 500 acres of land, receiving in payment of the value in cash, and the rest in a note due in 3 months without interest. He immediately discounted the note at a bank at 6%, paying $57.50 discount. What was the price of the land per acre?

178. How many slates will be required to cover a roof, each side of which is 34 feet 9 inches long and 16 feet wide, allowing 4 slates to cover a square foot; and what will they cost at the rate of $4.75 per C?

179. How many acres are there in a square tract of land containing as many acres as there are boards in the fence inclosing it, if the boards are 11 feet long, and the fence is 4 boards high?

180. Three men bought a grindstone 20 inches in diameter. How much of the diameter must each grind off so as to share the stone equally, making no allowance for the eye?

AVERAGE OF PAYMENTS.

470. 1. How long may $1 be kept to balance the use of $5 for 2 months? $6 for 3 months? $10 for 4 months? 2. How long may $10 be kept to balance the use of $6 for 5 months? $8 for 10 months? $12 for 5 months?

3. I owe B two equal debts, one due in 3 months and the other in 6 months. When may I pay both at one payment? 4. If I pay $20 3 months before it is due, how long after it is due may I keep $30 to balance it?

5. If I owe $20 due in 4 months and $40 due in 6 months, at what time are both debts equitably due?

471. Finding the equitable time for discharging, by one payment, sums due at different times is Averaging Payments.

472. The date at which the debts may be equitably discharged by a single payment is the Average Time.

473. The time that must elapse before the debt becomes Idue is the Term of Credit.

474. The time that must elapse before the debts due at different times may be equitably discharged by a single payment is the Average Term of Credit.

475. When the terms of credit begin at the same date.

1. A. T. Stewart & Co. sold a bill of goods upon the following terms: $400 cash, $300 due in 2 months, and $400 due in 4 months. At what time might the whole indebtedness be equitably discharged by a cash payment?

2200 mo.÷1100=2 mo. Average term of credit.

EXPLANATION. Since $400 was to be paid in cash, there was no term of credit for that sum. Since $300 Iwas to be paid in 2 months, the use of that sum for 2 months is equal to the use of

$1 for 600 months; and the use of $400 for 4 months is equal to the use of $1 for 1600 months. Hence, the credit of the whole debt, $1100, is equal to the credit of $1 for 2200 months, or $1100 for Tʊʊ part of 2200 months, which is 2 months, the average term of credit.

RULE.

Multiply each debt by its term of credit, and divide the sum of the products by the sum of the debts. The quotient will be the average term of credit.

2. The H. B. Claflin Co. sold a bill of goods amounting to $2300, on the following terms: $300 cash, $1200 due in 3 months, and the balance due in 4 months. What was the average term of credit?

3. Marshall Field sold a bill of goods payable as follows: $500 in 1 month, $ 500 in 2 months, and $800 in 4 months. What was the average term of credit?

4. Whitney & Co. sold a bill of lumber on the following terms: $1500 cash, $3000 payable in 30 days, and $2000 payable in 90 days. At what time will the debt be payable in one cash payment?

5. Thurber, Whyland & Co. sold to F. N. Burt a bill of goods amounting to $2400, payable as follows: in 30 days, the remainder in 60 days, and the balance in 4 months. What was the average term of credit?

6. Mr. Birge bought a bill of goods amounting to $3000, payable as follows: in 3 months, in 2 months, and the rest in 4 months. What was the average term of credit?

476. When the terms of credit begin at different dates.

1. Find the average time of payment of the following bills February 10, 1891, $400 due in 2 months; March 15, 1891, $350 due in 3 months; and April 12, 1891, $300 due in 3 months.

April 10+ 49 days May 29, average term. have $400 due

April 10, $350 due June 15, $300 due July 12. The average time when the bills will be due will be either after the earliest date, or before the latest date, and so we may select either of these dates from which to compute the average time. Selecting the earliest date, we find that $350 was due 66 days after that time, and $300 was due 93 days thereafter. Averaging, as in Art. 475, we find the term of credit to be 4814, or a fraction more than 48 days, which must be 49 days. This, added to April 10, gives May 29, the average time of payment.

RULE.

Select the earliest date at which any debt becomes due for the standard date, and find how long after that date the other amounts become due.

Find the average term of credit by multiplying each debt by the number of days from the standard date, and dividing the sum of the products by the sum of the debts.

Add the average term of credit to the standard date, and the result will be the average term of payment.

Instead of the earliest date, the first of the month may be used.

2. What is the average time at which the following bills become due: Feb. 1, 1887, $200 on 1 mo. credit; March 10, 1887, $500 on 3 mo. credit; April 12, 1887, $275 on 2 mo. credit; and May 1, 1887, $400 on 4 mo. credit?