Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

4

CASE IV.

303. Sum or Difference and Rate Per Cent

given to find the Base.

Oral Exercises +

EXAMPLE 1.- What number is that which if increased by 20% of itself, equals 48?

SOLUTION. -20% of a number = of the number, which added to for the number = & of the number, or 48.

Since 48 is & of the number, & of the number is of 48, or 8; and §, or the number, is 5 times 8, or 40. Therefore, 40 is that number to which if 20% be added the sum is 48.

EXAMPLE 2.- What number is that which diminished by 121% of itself, equals 56?

SOLUTION.-121% of a number = of the number, which taken from, or the number = of the number, or 56.

Since 56 is of the number, of the number is of 56, or 8; and , or the number, is 8 times 8, or 64. Therefore, 64 is that number from which if 124% be taken the difference is 56.

[blocks in formation]

4. 16% of itself = 35?

5. 150% of itself =

25?

11. My crop of beets this

10. 371% of itself = 200 ?

year was 42 bu., which was 5%

more than last year. What was it last year?

12. I harvested this year 450 bu. of wheat, which is 12+% more than my bins hold. What is their capacity ?

13. A man lost 20% of his sheep, and had 120 left. How many sheep had he at first?

14. Charles attended school 5 days in one week, which was 66% better than his brother James.. How many days did James attend?

15. A man bought stock to the amount of $4000, which lacked 20% of being all the money he had. How much money had he?

16. A farmer purchased a piece of land, containing 45 A., which was just 16% less than his farm. How many acres in the farm?

17. A merchant sold his bookkeeper an interest in his business for $4000, and then found that his own interest was 250% more than that of his bookkeeper. What was the value of his interest? Of both their interests?

+ Written Exercises+

EXAMPLE 1.- What number increased by 29% of itseli equals 1677?

1677

1ST SOLUTION.

1 + .29 = 1.29

1.29 = 1300

EXPLANATION. - Since the number

is increased by 29% or .29 of itself, 1677 is 129% or 1.29 times the num

the quotient 1300, or the number required, or base.

EXPLANATION.-Represent

ber: and 1677 divided by 1.29 gives

2D SOLUTION.

100% + 29% = 129% ;

1677129 = 13

[blocks in formation]
[blocks in formation]

EXAMPLE 2.- What number diminished by 31% of itself

[blocks in formation]

158769 = 23; 23 × 100 = 2300, Ans.

[blocks in formation]

EXPLANATION.The Base, 100%, -31% = 69% = 1587. 1% = 1587 69 = 23, and 100% = 100 times 23, or 2300. Or, by cancellation, we change 69 to .69 and divide, obtaining in both cases the same result, 2300.

304. RULE.-I. Divide the given number by 1 increased

or diminished by the given rate. Or,

II. Take such a part of the given number as 100% is of the sum or difference of 100% and the given rate %.

PROBLEMS.

What number

1. Increased by 13% of itself = 1582 ?

2. Increased by 171% of itself = 2350?
3. Increased by 22% of itself = 366 ?
4. Increased by 75% of itself = 787.5?
5. Increased by 125% of itself = 833+?
6. Increased by 325% of itself = 2210?
7. Increased by 22% of itself is 1098?

Ans. 1400.

Ans. 2000.

Ans. 300.

Ans. 450.
Ans. 37014.
Ans. 520.

What number

8. Diminished by 16% of itself = 700? 9. Diminished by 75% of itself = 125? 10. Diminished by 134% of itself = 260 ? 11. Diminished by 621% of itself = 131.25? 12. Diminished by 871% of itself = 284 ?

13. Diminished by 93% of itself = 12+ ?

Ans. 840.

Ans. 500.

Ans. 300.

Ans. 350. Ans. 225.

Ans. 200.

14. A drover bought 360 head of cattle, which was 25% more than he already had. How many had he before the purchase ? Ans. 288 head.

15. The average school term in Pa., in 1869, was 6.04 mo., which was 11.2% more than in 1863. What was the average term in 1863? Ans. 5.43 mo.

16. The average Pa. school term in 1863, was 5.43 mo., which was 10.05% less than in 1869. What was the length in 1869? Ans. 6.04 mo.

17. The distance by the P. R. R. from Pittsburgh to Harrisburg is 246 miles, which is 125% more than the distance by the same road from Harrisburg to Philadelphia. What is the latter distance? Ans. 109.2 mi.

18. W. R. Ford bought a farm for a certain sum, expended for stock 11% of the price of the farm, and found that the whole cost was $7215. What was the cost of the farm alone? Ans. $6500.

19. H. J. Gourley raised 800 bu. wheat, which was 25% more than of what Logan raised. How many bushels did Logan raise? Ans. 1280 bu.

20. A man dying bequeathed 10% of his property to his son, 20% of the remainder to his daughter, 334% of this remainder to his wife, and the remainder, or $48000, to charitable purposes. Required the value of the estate.

Ans. $100000.

305. Formulas.

The entire subject of Percentage may be summed up in

[merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

A thorough knowledge of the use of these formulas is about all the pupil needs to carry him through the Applications of Percentage; for by a simple substitution of the proper terms for B, P, R, &c., they can be made applicable to all cases except Interest, in which the element time (t.) is introduced.

306. Applications of Percentage.

Percentage is, because of its convenience, extensively used in business calculations. Its principal commercial applications are in Profit and Loss, Insurance, Commission, Interest, Discount, Stocks, Exchange, Taxes, Partnership and Bankruptcy.

« ΠροηγούμενηΣυνέχεια »