Abbildungen der Seite
PDF
EPUB

Page 255.

(3.)

Let a denote one number, and y the other.

Then, by the conditions,

[merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
[blocks in formation]

Substituting for 2, in Equation (2), we have,

16y+ y2+ y2 = 34;

[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]

Let a denote the first number, and y the second.

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

Substituting the value of y2, from Equation (1), we have,

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

(5.)

Let x denote the less, and y the greater.

Then, by the conditions,

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

and

34y2 41650;

=

y2 = = 1225; or, y = 35.

Hence, the numbers are 21 and 35.

(6.)

[ocr errors]

Let denote the less number, and y the greater. Then, by the conditions,

y x = 7; whence, y = x + 7,

[blocks in formation]

x(x+7)

2

+ 30 = x2; or, x2 + 7x + 60 = 2x2;

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

(8%)

Let the numbers be denoted by x and y.

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

Combining (1) and (3), we find,

x= 2, and y = 3.

(8.)

Let x denote the greater, and y the less.

Then, by the conditions,

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

Substituting these values of x and x2, in Equation (2), we

[blocks in formation]

Let a denote the distance, in miles, traveled by A, and y, the distance traveled by B.

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

Now, the rate of travel, or the distance traveled in a single day, will be found by dividing the distance by the number of days; hence,

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

Now, the entire distance traveled by A, divided by what he traveled in 1 day, will give the time he was traveling; and the same for B. But these times are equal; hence,

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

Substituting the value of 22, from Equation (1), we have,

[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][ocr errors][merged small]

which, after performing the operations indicated, gives,

y = 54, and, consequently, x = 72,

(11.)

Denote the less number by x.

Then the greater will be

denoted by x + 15; and we shall have,

[blocks in formation]
« ZurückWeiter »