WRITTEN EXERCISES Solve each of the following equations by first clearing of fractions. Check each answer for Exs. 1-15. Equations having denominators with several terms are solved in the same way as those having denominators with one term. SOLUTION. Multiplying both sides by x2-1, the L. C. M. of the denominators, gives 3x2−x−2+5 +5-9=3x–3. Canceling the 3 r2 and transposing, CHECK. Placing x= in the given equation, we obtain 1. Divide 64 into two parts such that if one part is divided by 5 and the other by 7, the sum of the quotients shall be 10. SOLUTION. Let x be one part. Then, 64-x= the other part. From the statement of the problem, we have 2. If 18 be subtracted from a certain number, three fourths of the remainder is 30. What is the number? 3. The difference between and of a certain number is 16. What is the number? 4. Divide 78 into two parts whose quotient is . 5. Divide 96 into two parts such that of the greater shall exceed of the smaller by 24. 6. The sum of two numbers is 179. If the larger is divided by the smaller, the quotient is 3 and the remainder 11. Find the numbers. [HINT. Let x=the larger number; then, 179-x=the smaller number. The equation becomes 7. Separate 286 into two parts such that the greater divided by the smaller gives a quotient 2 and a remainder 28. 8. One number is 222 greater than a certain other one. If the larger is divided by the smaller, the quotient is 3 and the remainder is 18. What are the numbers? 9. What number added to the numerator and denominator of will change the value of the fraction to &? [HINT. The equation is 3+x_6 Explain.] 10. What number added to the numerator and denominator ofwill change the value of the fraction to 18? 11. What number added to the numerator and denominator of will change the value to ? 12. What number added to the numerator and subtracted from the denominator of will change the value to ? 13. Two sevenths of a certain angle is 23° less than of its complement. How large is the angle (in degrees)? [HINT. The complement of an angle is the difference between 90° and that angle, i.e. the complement of any angle x is 90°— x.] 14. If of the supplement of a certain angle equals § of its complement, how large (in degrees) is the angle? [HINT. The supplement of an angle is the difference between 180° and that angle, i.e. the supplement of any angle x is 180°—x.] 15. The complement of a certain angle is of its supplement; find the angle. |
