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 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 4 ::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. 7 10x 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. 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, 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, Tr. & U. 3x=63, and x=21=younger son's share. 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 5x x 10 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 ber of yards in the second piece, XXXVIII. Let x=1 =the sum with which each began; then, x+40 x+40 =x- -40+ 3 2x+80 -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 == 3 2, 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. 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, 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. C. F. 80x=40x+288000+10x+48000+16x Tr. U. 80x-40x-10x-16x=288000+48000 14x=336000, and x=2400=the army. INVOLUTION. Example 5. Required the cube or 3d power of a+2d+3. a+2d+3=1st power. a2+4ad+ Ba+4d2+12d+9=2d power. a3+6a3d+9a2+12ad2 +36ad+27a+8d3 +36d2 +54d +27=3d power. |