24. Given 5+10 3x+4 x + = +43, to find the va25 2x-4 5 28. Given 4x+16=6, to find the value of x. Ans. x=5. 29. Given 8x+1+3=10, to find the value of x. Ans. x 6. 3 30. Given 4x-4+5=7, to find the value of x. Ans. x 3. 31. Given 2x+6+8=10, to find the value of x. Ans. x=5. 5 32. Given 7x+201-1=2, to find the value of x. Ans. x=6. 33. Given √x+7=7-x, to find the value of x. Ans. x=9. 34. Given x+9=1+/x, to find the value of x. Ans. x=16. 35. Given 4x+9=9-4x, to find the value of x. Ans. x=4. 36. Given 5x2+9=2x+√9, to find the value of x. Ans. x=12. 37. Given 9x+37=3√√x+1, to find the value Ans. x=36. of x. 42. Given 3y+4=√√/9y2+112, to find the va Ans. y=4. lue of y. 46. Given a+b=a+b to find the value of y. 47. Given a -y2 : √ a2_b2 √a+y, to find the value of y. :: √a2+b22 : Ans. y=b. THE APPLICATION OF SIMPLE EQUATIONS TO PROBLEMS OF ONE UNKNOWN QUANTITY. The method of solving algebraical problems or questions is to resolve them into equations, and then proceed by the general rules there given, In order to perform this, represent the quantity required, or some other quantity in the question, from which the required quantity may be found, by x or y, or any other letter of the alphabet, then perform with this letter and the given quantities in the question, by means of the common signs, the same operations and reasonings that it would require, or be necessary to make, if the quantities were known, and it was required to verify them, and the result will give an equation, which may be solved by the rules already laid down. To facilitate the progress of the pupil, the following examples, with their solutions, are given in a style as familiar as the nature of the subject admits : 1. A Lady was asked her age, who replied thus:My age, if multiplied by three, : Two-sevenths of that product tripled be, Here, the method of reasoning with her age is given in order to find it, from which it appears, that if her age could be known and operated with, as directed in the question, the four therein mentioned would be produced. (See the proof.) ... Let x = her age in years; then, 3x = her age multiplied by 3; PROOF. 3 84, her age multiplied by 3, 21 7)168 24, two sevenths of that product, 3 72, the product tripled, 2 9) 144 16, two ninths of the tripled product, 4, the square root of these two-ninths, as mentioned in the question; ... 28 answers the conditions of the question. 2. A Fish was caught, whose tail weighed 9lbs., his head weighed as much as his tail and half his body, and his body weighed as much as his head and tail. Required the weight of the fish? It appears from the nature of this question, that to substitute x for the weight of the whole fish would not conveniently answer the conditions of the question; but if the weight of the body was known, the other parts could be easily determined, and hence, the weight of the whole fish. 2 .. Let x = the weight of the body in lbs.';' then half the weight of the body, which being added to 9 lbs. (the weight of the tail) gives 9+the weight |