CHAPTER XX.

AVERAGES.

Ex. If a dozen eggs weigh 6668, what is their average weight?

Since the 12 eggs weigh 6668, the average weight of an egg will be of 666o = 55.5%.

The average weight is sometimes called the mean weight.

EXERCISE LXXVI.

1. If a dozen eggs weigh 6928, what is the mean weight of

2. Seven boys weigh respectively 119.7 lbs., 105 lbs., 178.3 lbs., 165.3 lbs., 142.8 lbs., 109 lbs., 154.2 lbs. What is their average weight?

3. A merchant mixes 1 lb. of coffee worth 27 cents, 1 lb. worth 35 cents, and 1 lb. worth 40 cents. What are the three pounds together worth? How much a pound is the mixture worth?

4. A merchant mixes 2 lbs. of coffee worth 27 cents a pound, 3 lbs. worth 35 cents a pound, and 1 lb. worth 40 cents. What is a pound of the mixture worth?

5. What is the value per pound of a mixture of coffee containing 7 lbs. worth 26 cents a pound, 4 lbs. worth 31 cents a pound, and 10 lbs. worth 34 cents a pound? 6. What is the cost of a gallon of the mixture in which 7 gals. cost 67 cents a gallon, 5 gals. cost 48 cents a gallon, and water, without cost, was added until there were 15 gals. of the mixture?

7. If 7' of water be poured into a vessel containing 31 of sulphuric acid, specific gravity 1.840, and the mixture shrink to 9.972, what is the specific gravity of the mixture?

8. If 4' of water and 1' of sulphuric acid, specific gravity 1.842, when mixed shrink of 1%, what is the specific gravity of the mixture?

Ex. In what proportion must alcohol of specific gravity .800 be mixed with water to bring the specific gravity to .925, if no allowance be made for condensation?

The specific gravity of the alcohol lacks .125 of the required specific gravity; and specific gravity of the water is 075 above the required specific gravity.

Therefore, the alcohol is to the water in the inverse ratio of 125 to 75. That is,

To test this answer: 31 of alcohol weigh 2.4kg, 51 of water weigh 5kg; therefore, 81 of the mixture weigh 7.4kg, and the specific gravity of the mixture is 74 = .925.

9. In what proportions must tin of specific gravity 7.29 and lead of specific gravity 11.35 be mixed to make a solder of specific gravity 10.21, if no allowance be made for expansion or condensation? (Give the proportions in bulk.)

10. In what proportions must oils worth $1.25 and 80 cents a gallon be mixed to make a mixture worth $1 a gallon? (Test the answer.)

11. In what proportion may oils worth $1.20, 80 cents, and 60 cents a gallon be mixed so that the mixture shall be worth 70 cents a gallon?

The price of the mixture may be brought to 70 cents by adding to the 60-cent oil either of the better oils, or both mixed in any proportion.

When the 80-cent oil alone is taken, in what ratio to the 60-cent must it be used? When the $1.20 oil alone is taken, in what ratio to the 60-cent oil must it be used? When the $1.20 and 80-cent oils are mixed gallon for gallon, how much 60-cent oil must be added? When 1 gal. of the $1.20 oil and 3 of the 80-cent oil are taken, how much 60-cent oil must be added? If three-fourths of the mixture consist of the 60-cent oil, what per cent of each of the other two must be taken?

12. A solder composed of tin and lead, specific gravities 7.29 and 11.35, has a specific gravity of 10.44. What is the weight of each metal in a kilogram of solder?

AVERAGE OF PAYMENTS.

Ex. John Smith has given to William Jones notes as follows: $150, due May 15; $200, due June 30; $500, due July 21. He wishes to pay them all at one time. When shall they be considered due?

If all the notes were paid May 15, Smith would lose the use of $200 for 46 days, and of $500 for 67 days.

=

The use of $200 for 46 days is equal to the use of $200 × 46 for 1 day; and the use of $500 for 67 days is equal to the use of $500×67 for 1 day. Smith would, therefore, lose what is equivalent to the use of $9200 + $33,500 = $42,700 for 1 day, and is entitled to keep the $150 + $200 + $500 $850 as many days after May 15 as are required for the use of $850 to equal the use of $42,700 for 1 day, or 43700 days = 50.2 days. Hence, the equated time for paying all the notes is 50 days after May 15; that is, July 4.

The work may be arranged as follows:

13. Find the equated time for the payment of $250 due in 3 mos., $400 due in 6 mos., $700 due in 8 mos.

14. Find the equated time for the payment of $300 due in 30 dys., $500 due in 60 dys., and $200 due in 90 dys.

15. Find the equated time for the payment of $325 due now, $200 due in 30 dys., $460 due in 60 dys., and $150 due in 90 dys.

16. Find the equated time for the payment of $240 due May 10, $420 due July 2, $310 due Sept. 14, and $600 due Oct. 1.

17. Find the equated time for the payment of $275 due June 21, $175 due July 16, $200 due Aug. 6, and $150 due Sept. 3.

18. Find the equated time for the payment of $112.30 due July 6, $115.25 due July 30, $232.15 due Sept. 4, and $102.36 due Oct. 1.

Ex. A owes B $200 due in 10 mos. If he pays $120 in 4 mos. when should he pay the balance?

By paying $120 in 4 months A loses the use of $120 for 6 months, which is equal to the use of $720 for 1 month. Therefore, he is entitled to keep the balance ($80) 720 months months after its maturity.

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19. A owed B $2000 payable in 4 mos., but at the end of 1 mo. he paid him $500, at the end of 2 mos. $500, and at the end of 3 mos. $500. In how many months is the balance due?

20. A merchant bought, Feb. 11, 1881, a bill of goods amount

ing to $1700, on 4 months' credit; but he paid Mar. 22, $400, Apr. 20, $220, May 10, $300. When is the balance due?

Find the equated time of maturity of each of the following bills, and the amount due at settlement, including interest at 6%:

JAMES PRICE, to JOHN BATES, Dr.

21.

Find the equated time for payment, reckoning from July 15, which is the earliest date that any item becomes due, and find the interest on the whole bill from the equated time to Oct. 18. As this is not banking business, allow no days of grace.

23. Find the equated time of maturity of each side of the

NOTE. On the Dr. side is the statement of the goods sold by Bacon & Co. to Adams & Co.; and on the Cr. side is the statement of the cash paid by Adams & Co. to Bacon & Co.