. High school algebra . and 6 =-I. what are the values of a+6, ab, ti ^, a»+6», a»-6» 7ab ALGEBRAIC NOTATION 16 36. li A can do a piece of work in 10 days and S in 15 days, whatfraction of the work can they together do in 1 day ? What fractionif A could do it in x days and B in y days ? 37. If a = 20, 6=15, c=10, d = 5, find the difference between(0+6) —(c+d) and (o —6) —(c —d), also between 3(a+6) —5(c —d) and6(0-(f)-3(6-c). 38. When x = 7 and y=\, the product of x-\-y, x+2y, x — by is howmuch greater than the product of x — y, x—2y, x—3y ? 39. If 0 = 3, find the value of 1 -\ ^ • CHAPTER II
. High school algebra . and 6 =-I. what are the values of a+6, ab, ti ^, a»+6», a»-6» 7ab ALGEBRAIC NOTATION 16 36. li A can do a piece of work in 10 days and S in 15 days, whatfraction of the work can they together do in 1 day ? What fractionif A could do it in x days and B in y days ? 37. If a = 20, 6=15, c=10, d = 5, find the difference between(0+6) —(c+d) and (o —6) —(c —d), also between 3(a+6) —5(c —d) and6(0-(f)-3(6-c). 38. When x = 7 and y=\, the product of x-\-y, x+2y, x — by is howmuch greater than the product of x — y, x—2y, x—3y ? 39. If 0 = 3, find the value of 1 -\ ^ • CHAPTER II SIMPLE EQUATIONS 12. Idea of Equality. In weighing an article, when yousee that the scales are balanced, what conclusion do youdraw ? If a 5 lb. bag of salt is placed in one scale pan, whatweight (w) must be placed in the other pan to restore thebalance ? What must w be to balance a 3 lb. bag and a4 lb. bag ? If the scales are balanced in each of the following figures,what must w be equal to ?. Fia. 1. Pio. 2. Fio. 3. If U)+4 = 9, as in fig. 1, what is w equal to ? If w-\-io= 12, as in fig. 2, what is iv equal to ? If 1^+3 = 5+2, as in fig. 3, what is w equal to ? If the scales are balanced and I add 2 lb. to one side, what else mustI do to preserve the balance ? What, if I take away 3 lb. from one side ?If I double the weights on one side ? If I halve the weights on one side ? 13. The Equation. When a certain number is added to10 the result is 27. What is the number ? The condition expressed in this problem might be morebriefly shown in the form : 10+a certain number=27,or in the form 10+?=27, where the question mark stands forthe required number. Any other symbol would answer the same purpose as the SIMPLE EQUATIONS 17 question mark. Thus, if x represents the required number,then the problem states that 10+a;=27. This statement is called an equation and is merely a shortway of stating what is given in the arithmetical problempreceding. In order that
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