MATHEMATICS. ALGEBRA. [HOLUTIOSS TO THE EXERCISES. 



Multiplying by 3, 3x + 2x - fi - 6 0, or 5x --- " 6. 



"' i 

 by6, 25r 6x-30, .-. 19x-30, ..x-7" = iu 



Y+ ----0. Multiplying by 2, 



x+ 3 2 1 =0. 



3* 3z 



3 = 0, or5x - 3-0. 



Multiplying by 3, 



by 2, lOx 3x 6-0, .. 7x-6, .'.a 



21. 11 a '- ., 3-. Multiplying by 8, 



Multiplying by 3, 264 16z = 12x 16*, . . 264 = ILe, . . x . 



22. 4x 2 (3 x) =^-, that is, 4x 6 + 2x = ^-^, or Gx 6 = ~^. 



Multiplying by 2, 12* 12 

 = -g-. Multiplying by 5, 



3, .-. llx = 15, . . x, = ~ = 



24 



30x 4+ 3* = 29, .-. 33* = 33, .-. x = 1. 



x x^2 xxx x 



+ -g- = 20 2 , that is, -^ 3 + -3- = 20 ^- -f- 1, or by transposing, x+ -- = 21, .'. mult 



by 3, ar + x = 72, . . 4x = 72, .' . x = 18. 



O ^^ 1 Q 1 ! ^^ A^ 



25. - - H 3 0. Multiplying by 7, 



. 77 2&e 



3x 13 H = 0. 

 o 



Multiplying by 3, 9* 39 + 77 28x = 0. 

 Transposing, 38 = 19*, . . x = 2. 



26. 6 2 _- = -, Multiplying by 4, in order that both the first and last fractions may be 



cleared at tho same time, we have 



Multiplying by 3, 72 Gz + 6 4x + 8 = 9 3x. 



Transposing, 72 + C + 8 9 = 6x + 4z 3z. 



Collecting, 77 = 7x, . . x = 11. 



QUESTIONS TO BE SOLVED BY SIMPLE EQUATIONS. 

 PAGE 458. 



1. There are two numbers of which the difference is 

 9, and tho sum 43. What are the numbers ? 



Let x represent tho smaller of the two numbers, then 

 by tho question, the other must be x + 9, and their 

 turn 



x + x + 9 - 43, that is, 1x = 43 9, 



' x ~_~2 ** 17 > 



iho smaller number, and .. 17 + 9 = 26, tho larger 

 number. 



2. From two places, 108 miles apart, two persons, A 

 and I!, set out at the same time, to meet each other. A 

 travels 17 miles a-day, and B travels 18 ; in how many 

 days will they meet ? 



Suppose they moet in x days: then by tho question, 

 the first, A, will have travelled 17* miles, and the 

 second, B, 18x miles ; and since the sum of these 

 distances is the distance between the two places, we 

 have tho equation 



\~f. + 18x - 108, .-. 35x = 108, .-. x - 3& days. 



3. Find two numbers or which the difference is 13, 

 and which are such, that if 17 bo added to their sum, 

 the whole will amount to 62. 



Let x bo the greater number ; then, by the question, 

 x 13 ii the lew ; also 



x + x 13 + 17 = 62, .-. 2e = 02 + 13 17 = 58, 

 .. x = 29, tho greater number, and . '. 29 13 = 16, the 

 less number. 



4. There are two numbers of which the difference is 

 15, and which are such that if 7 times the loss bo sub- 

 tracted from 5 times the greater, the difference will be 

 19 : what are the numbers ! 



Let x be the greater number ; then, by the question, 

 x 15 is tho less ; also 



5.e (7x 105) = 19, that is, 2x + 105 - 19, 



. . 2x - 80, 



Qy 



. . x = -= 43, tho greater number, and 

 . . 43 15 = 28. tho less number. 



5. A person starts from a certain place, and travels at 

 the rate of 4 miles an hour. After lie has gone 10 hours, 

 a horseman, riding 9 miles an hour, is dispatched after 

 liiiu : how many hours must tho horseman ride to over- 

 take him ? 



Suppose tho horseman overtakes him after riding x 

 hours ; then, by the question, tho pedestrian will have 

 walked 40 + 4r miles, and tho horseman will have 

 ridden !)j; miles ; and since tho distance travelled by 

 uach is tho same, we have the equation 



Qx - 40 -f- 4x, . . 5x - 40, . '.x - 8 ; 



