Imágenes de páginas
PDF
EPUB
[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][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][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

1. A man placed of his capital at 5% and the other third at 6%. At the end of a year, capital and interest amounted to $31,600. What was his capital?

[blocks in formation]

2. A has 18 chestnuts more than B. If each finds 4 more, A will have four times as many as B.

each?

How many chestnuts has

3. Two mechanics earn together $8 per day. One works 23 days and the other 17 days, for which they receive together $166. What does each earn per day?

4. The sum of the first and the second of three numbers is 55, of the first and the third 62, of the second and the third 83. What are the numbers?

5. The sum of two numbers is 53. Four times the first is 20 more than twice the second. Find the numbers.

6. A certain sum of money is divided among four persons. The first takes of it, the second takes of the remainder, the of what then remains, the fourth receives the What is the share of each of the other three?

third takes balance, $24.

7. A merchant sold a lot of goods for $510, thereby losing 2 of their cost. What did the goods cost?

8. A man collected a bill for a physician and deducted of the amount for his services. If he gave the physician $147, what was the amount collected?

9. Divide 130 acres of land among three persons, giving the first 27 acres more than the second, and the second 13 acres more than the third.

10. A merchant has sold 4 of a piece of cloth, and has remaining 16 yards more than of the piece. How many yards did the piece contain originally?

11. A servant is engaged for a year for $280 and a suit of clothes; he leaves at the end of six months, and receives $130 and the suit. What is the value of the clothes?

MULTIPLICATION OF ALGEBRAIC QUANTITIES.

1225. Multiply x + 3 by x + 4.

The product is equal to x times (x+3)+4 times (x+3).

x(x+3)= x2+3x

4(x+3)= 4x+12

(x+3)(x+4)= x2+7x+12 Ans.

NOTE.—x2 is read x square. The 2 is called an exponent.

[blocks in formation]

1228. Find products:

(3x+1) by (x+7) 6. (2x+1) by (2x+1)

x-5

x +4

[ocr errors]

5x

4 x

20

x2-x-20 Ans.

NOTE.-(x-3) (x + 9) means x · 3 multiplied by x + 9.

7. (x 3)(x+9) 10. (x+5) (x − 5)

8. (x−6)(x+7) 11. (2x-6) (x + 1)

13. (2x−6) (3x+3)

14. (3x+6) (2 x −3) 9. (x-5)(x+5) 12. (x-6) (2x+1) 15. (2x+3)(2x-3)

1229. (x-5) (x-4)=?

The product is equal to x(x-5) — 4(x -- 5); that is, that 4(x-5) is to be subtracted from x(x-5).

x(x-5)= x2-5 x; 4(x-5)=4x-20.

Placing the subtrahend under the minuend, and changing the signs of the former (Art. 1209), we have

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

1230. (x-7)(x-9)=?

[ocr errors][merged small]

x2,

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

Using either as a multiplier, place one under the other. Commencing with x, say x×x= -9x=-9x. Taking - 7 as a multiplier, say xx (-7)=-7x, (−9) × (−7) = 63. ing, we get the product.

Combin

Ans. x2-16x+63

1231. Note that the multiplication of a +(positive) quantity by a + (positive) quantity gives a +(positive) product; that (+) x (−) or (−) × (+) gives a — (negative) product; and that (-) (-) gives a + (positive) product. This is usually stated as follows:

[ocr errors]

1232. Like signs produce +, and unlike signs produce -.

1233. Give results:

20. ( x+7)( x −6) 24. (2x+7)(3x+3)

16. (x −7) (x −7)

17. (x — 5) (x — 9)

21. ( x−4)( x

25. (2x-3)(3x-2)

18. (x+5)(x+5) 22. (2x-4)(3x-6)

26. (2 x − 3)(2x+3)

19. (x-3)(x+8) 23. (2x+6)(3x-7) 27. (2x+9)(4x-6)

[merged small][ocr errors][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]

1235. Since (8) x (-8)= 64, the square root of 64 may be either +8 or 8. It is written ± 8, and is read "positive or negative 8." (It is sometimes less correctly called plus or minus 8.)

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

1. Find the dimensions of a field, the length of which is twice its breadth, its area being 1,800 square rods.

2. The surface of the six equal faces of a cube contains 96 square inches. Find the length of one edge.

3. One number is fourth-fifths of another, and their product is 80. What are the numbers?

4. One-third of a number multiplied by two-fifths of the same number gives a product of 270. Find the number.

5. Thirty per cent of a number multiplied by forty per cent of the same number gives a product of 300. What is the number?

« AnteriorContinuar »