(1) 2 lb. additional are placed on each plate; or, (2) 2 lb. are taken from each plate; or, (3) 2 × 6 lb. are placed on each plate; or, (4) 6 lb. 2 are placed on each plate. 204. Section 203 illustrates the following: (1) If equals are added to equals, the results are equal. (2) If equals are subtracted from equals, the results are equal. (3) If equals are multiplied by equals, the results are equal. (4) If equals are divided by equals, the results are equal. 205. If x stands for 4, (1) 6x-2=3x+10. (2) 6x-10=3x+2. · In equations (1) and (2) observe that the 2 and also the 10 are in different members, and that the signs before each of these numbers are different in the two equations; hence: 206. A term may be transposed from one member of an equation to the other, if the sign before it is changed. Exercise 61 1. If x+6=8, for what number does x stand; that is, what is the value of x? x+6=8 x=8-6 [§ 206] In each of the following find the value of x: 14. If 5x=40, what is the value of x? 5x=40 Dividing by 5, x=8 [§ 204, 4] 15. If x=4, what is the value of x? 3 x = 4 Multiplying by 3, x=12 [§ 204, 3] 16. If x=4, what is the value of x? 3 x = 4 Multiplying by 3, 2x=12 [§ 204, 3] 4. 3=x+2 7.5=x-2 10. 1-x-1 13. 5=x+3 In each of the following, find the value of x: 41. If 4x-3=2x+9, find the value of x. 4x-3=2x+9 Transposing, 4x-2x=9+3 Uniting terms, 2x=12 Dividing by 2, x=6 In each of the following find the value of x: The sum of two numbers is 25, and the larger is 4 times the smaller; what are the numbers? Exercise 62 1. The sum of two numbers is 30, and the larger is 4 times the smaller; what are the numbers? 2. The sum of two numbers is 15, and the smaller is of the larger; what are the numbers? 3. Two girls have 50%; if one of them has 4 times as much as the other, how much has each? 4. A woman bought a certain number of yards of lining and twice as many yards of dress goods; if she bought 30 yd. of both, how many yards did she buy of each? 5. A and B together own 350 acres of woodland; if A owns 4 times as much as B, how much does each own? 6. An article was sold at a gain of $12, which was 1 of the cost; what was the cost? 7. An article was sold at a loss of $2.50, which was of the cost; what was the cost? 8. A dealer sold an article for $300, which was at a gain of of the cost; what was the cost? 9. An article was sold for $75, which was at a loss of of the cost; what was the cost? 10. Two men together bought 65 head of cattle; if one of them bought 5 head more than the other, how many did each buy? II. After a man had sold of his land to one man and of it to another, he had left 220 acres; how much had he at first? PERCENTAGE 207. Per cent means hundredths. Thus, 1 per cent of a number is .01, or, of it. 100 The sign % stands for per cent. Thus, 6 per cent of 25 may be expressed 6% of 25. 208. The number or amount of which a given per cent is taken is called the base. The number of hundredths of the base taken is called the rate per cent, or the rate, and the result obtained by taking a given per cent of the base is called the percentage. |