and 324 marks in Germany. What is my total indebtedness in United States money? 8. What is the gain on 2500 yd. of English woolens bought at 38. 6d. per yard, and sold at $1.40 per yard? 9. What is the gain in U.S. money on a French automobile costing 8000 francs, if sold in England for £ 420? 10. A druggist bought 200 lb. (commercial weight) of chemicals at 31 per pound. What is his gain if he sells at 42¢ per pound (apothecaries' weight)? 7. What will be the cost of 25 bath robes at $2.50 each? 8. What will be the cost of 15 squares of gravel roofing at $1.50 per square? 9. A retailer bought $40 worth of cotton goods at 61¢ per yard, and sold the lot at 12 per yard. How much did he make? 10. I bought 300 articles at 331 each, and sold them at 50 each. How much did I gain? THE EQUATION 126. If weight in one pan of the scales exactly balances a quantity of sugar in the other pan, we may say that in respect to weight, the four-pound weight is a four-pound 4 lb equal to the sugar. A statement that one quantity is equal to another quantity is called an equation. The sign of equality (=) is read "equals." 127. The equation is used for abbreviating statements : Thus, the question, "If a 50-acre farm is worth $5000, what is 1 acre worth?" can be abbreviated to read: "If 50 A. $5000, what does A. equal?" = Further, the statement that, “If 50 acres are worth $5000, 1 acre is worth 1-50th of $5000, or $100," can be abbreviated to read: 128. If 50 A. = $5000, what will 100 A. =? 129. Further illustrations might be given to indicate that any operation may be performed on both sides of an equa tion without destroying its value. rive the following important rules : From this fact we de (a) Dividing both sides of an equation by the same number does not alter the value of the equation. (6) Multiplying both sides of an equation by the same number does not alter the value of the equation. (c) Adding the same number to both sides of an equation does not alter the value of the equation. (d) Subtracting the same number from both sides of an equation does not alter the value of the equation. (e) Squaring both sides of an equation does not alter the value of the equation. (ƒ) Taking the square root of both sides of an equation does not alter the value of the equation. 130. If, in the equation 50 A. = $5000, the value of A. ($100) is put in place of A., we get the following statement: 50 x $100 = $5000. This process is called substitution. It is used in checking the work, and in the application of formulas. page 94.) (See § 147, 131. Solution of problems by the equation. In the equation 50.A. = $5000, we found that A. = $100, or we say that we have solved the equation for the value of A. 1. Solve for x in the equation 4 x = Dividing by 4, · 20. x = 5. If the division cannot be performed, indicate it thus: Solve for x in the equation be = 20 (bx means b times x). 3. Solve for x in the equation 2x+5=x+15. Subtracting 5, Subtracting x, 2 x = x + 10. x = 10. 2x = 20. x = 10. 4. Solve for x in the equation 2x-4=16. Adding 4, Dividing by 2, Substituting 10 for x, (2 × 10)-4=16 (check). NOTE. Add or subtract until the left-hand side of the equation has only the term containing the unknown. 5. Solve for x in the equation Extracting square root, 2 = 16. x = 4. 6. Solve for x in the equation √x=3. 26. If h = 4 and A = 16, find B in ¦ Bh = A. 27. If B3 and h = 4, find H in H2 = B2 + h2. 28. If h = 3, k = 12, K = 16, and A = 40, find P in Ph+ k+K=A. 29. If K= 15 and V= 45, find h in } hK= V. 30. If (called pi) = 3.1416 and A28.2744, find r in ngủ = A. = If a 3, b = 4, and e= 5, find x in the following: |