be added to the number, the digits will be inverted. What is the number?

35. A man has money in dwo drawers, and $25 in his purse. Now, if he put his purse into the first drawer, it will contain as much as the second; but if he put his purse into the second drawer, the sum in the first will be to the sum in the second as 5 to 13. How much is there in each drawer ?

36. Two clerks, A and B, send ventures, by which A gained $20, and B lost $50, when the former had wice as much as the latter; but had B gained $20, and A lost $50, then B would have had 4 times as much as A. What sum was sent by each?

37. A farmer, having mixed a certain quantity of barley and oats, found that, if he had mixed 6 bushels more of each, he would have put into the mixture 7 bushels of barley for every 6 of oats; but if he had mixed 6 bushels less of each, he would have put in 6 bushels of barley for every 5 of oats. How many

bushels did he mix?

38. A person has a gold watch and a silver one and a chain for both worth $8. Now, the silver watch and chain are together worth half as much as the gold watch; but when the chain is on the gold watch, they are together worth 3 times as much as the silver watch. What is the value of each?

39 If a certain volume contained 12 more pages, with 3 lines more upon a page, the number of lines would be increased 744; but if it contained 8 pages less, and the lines on a page were not so many by 4, the whole number of lines would be diminished 680.

How many pages are there in the book? and how many lines on a page?

40. Two neighbors, A and B, possess 562 acres of land. If A's farm were 4 times, and B's 3 times, as large as each of them is, they would both together have 1924 acres. How many acres has each?

41. Two men owe more money than they can pay. Says A to B, "Give me of your property, and I shall be able to pay my debts." "If you will give me of yours," replies B, "I shall be able to pay my own." The amount of A's debts is $1500, and of B's, $2125. How much property has each in his possession?

42. A trader bought at auction two pipes containing wine. For one he gave 8s. a gallon; for the other, 10s. 6d. ; and the whole came to $160. Having sold 25 gallons from the first pipe, and 16 gallons from the second, he mixed the remainder together, and added 15 gallons of water. Afterwards, 5 gal

lons of the mixture leaked out; and the remainder was worth 8s. a gallon. How many gallons did each pipe contain?

43. A man had 32 gallons of wine, in two barrels. Wishing to have an equal quantity in each, he poured out of the first into the second as much as it already contained; again, he poured out of the second into the first as much as it then contained; and, finally, he poured out of the first into the second as much as still remained in it. Each barrel then contained the same quantity. How many gallons did they contain originally?

SECTION VII.

Three or more Unknown Quantities.

1. Three boys, A, B and C, bought fruit at the same time. A bought 4 oranges, 7 peaches and 5 pears, for 51 cents; B bought 6 oranges, 8 peaches and 10 pears, for 74 cents; and C bought 9 oranges, 3 peaches and 2 pears, for 58 cents. What was the price of each?

Let

the price of an orange,

y = the price of a peach,

and z = the price of a pear.

A. Then 4 x + 7y+ 5 z = 51, by A's purchase B. 6x+8y + 10 z = 74, by B's,

c. 9x+3y+2 z 58, by C's.

=

These unknown quantities must be made to disap pear, one at a time. Either method of elimination, explained in the last section, may be used. We must, in the first place, deduce, from these three equations, two others, which shall contain but two unknown quantities each.

If we multiply equation a by 2, the coefficient of z will be the same as it is in equation B.

D. 8x + 14 y + 10 z

B. 6x+8y + 10 z =

E. 2x+6y *

102

74

28,-by subtraction.

F. x + 3y = 14, by division.

Again, if we multiply c by 5, the coefficients of z

We have now two equations, namely, r and н, which contain only two unknown quantities.

If we substitute this value of x in equation н, we shall have

546

K. 39 (14—3 y) + 7y = 216.

117 y + 7y = 216, by multiplication. 546216 117 y7 y, by transposition. 330 110 y, by reduction of terms.

L. y 3, by division.

=

If we substitute this value of y in equation F, we shall have

x + (3 × 3) = 14.

M. x 14 9 5, by transposition.

95,

And if we substitute the values of x and

y, as determined in L and м, in any of the preceding equations

M,

containing z, we shall obtain the value of that quantity. Take equation c, for instance.

c. 9 x 5 +3 × 3 + 2 z =

or 45+9+ 2 z = 58.

58,

4, by transposition

2z58459

and z = 2.

ANS. An orange, 5 cents,

A peach, 3 cents;

A pear, 2 cents.

2 A fruiterer sold to A 5 oranges, 6 peaches and 7 pears, for 75 cents; to B 8 oranges, 9 peaches and 5 apples, for 94 cents; to C 2 oranges, 8 pears and 10 apples, for 56 cents; and to D 3 peaches, 6 pears and 9 apples, for 48 cents. What was the price of

each?

To solve this question, we must use four unknown quantities; but their values may be found according to the principles already explained. It will be observed, that all the unknown quantities do not enter into each of the equations.

and z = the price of an apple.

A. Then 5 + 6x + 7y = 75, by A's purchase,

B.

v

8 v + 9 x + 5 z = 94, by B's,

c. 2 v + 8 y + 10 z = 56, by C's,

D. 3x+6y+9z 48, by D's.

=

c. 2 v + 8 y + 10 z = 56,

or 2v 56-8 y

=

E. and v = 28

10 z, by transposition,

By substituting this value of v, in equations a and ve have