The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

ing then if A travels 10 miles an hour, 10x=the distance A travels. If B travels 8 miles an hour, 8x=the distance

10x+8x=360, and x=20hours time of travel. A travel.

ed 10 miles an hour, therefore 10×20=200, A's distance; and 8×20=160=B's distance.

C. F. 12x=4x+3x+240, and 5x=240, and x=48.

XXI. Let x=the length of the post: then,

x 3x
x=1+. +13.
5 7

C. F. 35x=7x+15x+455, and 13x=455, and x=35.

XXII. Let x=the required number: then,

=100.

C. F. 3x+30=330, and 3x=300, and x=

XXIII. Let x=1 =the whole number in the orchard: then,

XXIV. Let x=the number of gallons: then,

20:

x-7

::94 x 80: x-7::376: 4x.

1. C. P. 320x=376x-2632.

2. Tr. & U. 56x=2632, and x= 47 the number of gallons.

XXV. Let x=the income of each: then,

10x

10x- +10x + +160=2x=the income of both.

10x
5

1. C. F. 350x+70x+350x-50x+5600-700x.

2. Tr. & U. 20x=5600, and x= =$280=the income of each.

XXVI. Let x=the age of the father: then,

C.F. 14x+8x+280+28x+224=56x-50.
Tr. & U. 6x=504, and x=84-the father's age.

XXVII. Let x=the required number: then,

1. C. F. 10x=2x+1000+5x+350

2. Tr. & U. 3x=1350, and x=450-income.

XXIX. Let x=the amount of gun powder: Then,

1. C. F.

2. Tr.

5292x=3528x+52920+882x-23814+504x+

7560-105844

5292x-3528x-882x-504x=52920—23814+

7560-105844

3. U. 378x=26082, and x= =69=amount of gun powder.

XXX. Let x=the number of gallons of brandy: Then, x+x+15+2x+15=146

Tr. & U. 4x=116, and x=29=the brandy: and 29+15= 44 the wine; 146-29+44-73-the water.

XXXI. Let x=what A paid: Then,
x+3x+4x+6x+x=4755

Tr. & U. 15x=4755, and x= -317-A's payment.

XXXII. Let x=the first part; Then,

æ+æ–3+æ+10+æ-9+2+16=99

Tr. & U. 5x=85,and x=17=the first part.

XXXIII. Let x=the younger son's share: Then,
ætæ+9+æ+21+2+39=7æ+6

Tr. & U. 3x=63, and x=21=younger son's share.
Then 7x21+6=153=what the father distributed.

XXXIV. Let x=the number which each flock originally contained; Then, X- -39=x-93 × 2

Expanding x-39=2x-186, and x=147.

XXXV. Let x=the number of days in which the latter express would overtake the former; Then,

x: 300::1:15, and 15x=300, and x=20.

XXXVI. Let x=the age of C; then 3x=B's, and 6x= A's; Then, x+3x+6x=140, and x=14=A's age, 14 x3=42=B's age, 42 × 2=84=A's age.

XXXVII. Let x=the number of yards in the first piece,

13x

the price per yard, and. No. yards in second

2. C. F. 60x+600=65x+500

3. Tr. & U. 5x=100, and x=20=No. of y'ds

in first piece. And =26, which the num

13x
10

ber of yards in the second piece,

XXXVIII. Let x=1 =the sum with which each began; then,

x+40

=x- -40+

2x+80
3

-40

C. F.

3x+120+x+40=3x-120+2x+80-120,

and x=320.

XXXIX. Let x=the required number; Then,

36+x: 52+x::3:4

C. P. 144+4x=156+3x, and x=12.

XL. Let x=the harness; Then,

x+2x+6x=360, and x=$40=the harness, $40×2 =$80=the horse, 360-120=$240=the chaise.

XLI. Let x=the number of gallons contained in the cask; and 2x+126=3x, and x=126.

Then, +21 ==

XLII. Let x=the age of the youngest; Then, x+20= the age of the eldest. Then 3x=x+20, and x=10 the age of the youngest.

XLIII. Let x=the greater number; Then, 49-x=the Then, x+6: 49—x−11::9: 2

less.

C. P. 2x+12=441-9x-99, and 11x=330, and x=

XLIV. Let 2x=the less, and 3x=the greater; Then, 2x+4: 3x+4::5:7

-30.

C. P. 14x+28=15x+20, and x=8, and 2×8-16= the less; and 3×8=24⇒the greater.

XLV. Let x=the number of gallons in the less, and 3x= the number of gallons in the greater; Then, x-4×4=3x-4, and 4x-16=3x-4, and x=12=the less, and 12×3=36=the greater.

XLVI. Let x=the less number; Then,

68-x-84—3x-120, and 4x=104, and x=26=the less.

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2x+6x=408-60x=68x=408, and x=6.

2x=12 A to B, and 3x=18 C to D, and 34-5x-4 B to C.

XLVIII. Let x= = of the first; Then,
2x+3x+4x=36, and x= =4= the first.
=8, the second=12, and the third=16.

Then the first

XLIX. Let 27x+200=the whole stock; Then, 27x+150+9x+50=36x+200-amount end 1st year. 36x+150+12x+50=48x+200=

2d year.

48x+150+16x+50=64x+200= am't end. 3d year. By the conditions of the problem this last expression= twice the original stock, which is 27x+200; Hence, 27x+200x2=64x+200

Multp. 54x+400=64x+200

Tr. & U.

200=10x, and x=20; and 27x+200=

740 the original stock.

The following is a more common statement, but the solution is tedious on account of its great length.