Let a denote the less number, and solve the question again. Note. Observe, that after multiplying by 5 in the above example, the signs of both terms of the numerator were changed, that of 408 to, and that of 2 x to +; this was done because it was not required to subtract so much as 408 by 2x. The change of signs could not be made before multiplying by 5, because the sign — before the fraction showed that the whole fraction was to be subtracted. If the signs of the fraction had been changed at first, it would have been necessary to put the sign+before the fraction. This requires particular attention, because it is of great importance, and there is danger of forgetting it. 7. A man bought a horse and chaise for $341. Now if of the price of the horse be subtracted from twice the price of the chaise, the remainder will be the same. as if of the price of the chaise be subtracted from three times the price of the horse. Required the price of each ? Ans. Horse $152, chaise $189. 8. Two men, A and B, were playing at cards; when they began, A had only as much money as B. A won of B $23; then of B's money, subtracted from A's, would leave one half of what A had at first. How much had each when they began? Ans. A had $45, and B $75. 9. A man has a horse and chaise. The horse is worth $44 less than the chaise. If of the value of the horse be subtracted from the value of the chaise, the remainder will be the same as if from the value of the horse you subtract of the excess of the value of the horse above 84 dollars. What is the value of the horse? Ans. $126. VII. The examples in this article are intended to exercise the learner in putting questions into equation. They require no operations which have not already been explained. It was remarked, that no rule could be given for putting questions into equation, but there is a precept which may be very useful. Take the unknown quantity, and perform the same operations on it, that it would be necessary to perform on the answer to see if it was right. When this is done the question is in equation. 1. A and B, being at play, severally cut packs of cards so as to take off more than they left. Now it happened that A cut off twice as many as B left, and B cut off seven times as many as A left. How were the cards cut? By the conditions,7 times 52- 2 x are equal to 52-x. Ans. A cut off 48, and B 28. Take the numbers 48 and 28 and endeavour to prove that they are right, and you will see that you take the same course as above. 2. A man, at a card party, betted 3s. to 2 on every deal. After twenty deals he had won 5 shillings. At how many deals did he win? Let the number of deals he won. Then 20x the number of deals he lost. = Every time he won, he won 2 shillings; that will be 2 x shillings. 20 Every loss was 3 shillings; that will be 3 times The loss must be taken from the gain, and he will have 5 shillings left. 2x60+3x=5. Ans. 13 deals. 3. What two numbers are to each other as 2 to 3; to each of which, if 4 be added, the sums will be as x Adding 4 to each, they become a + 4, and 3*+ 4. 2 The first is now of the second, or the second is 4. A sum of money was divided between two persons, A and B, so that the share of A was to that of B as 5 to 3. Now A's share exceeded of the whole sum by $50. What was the share of each person? Ans. A's share $450, B's $270. 5. The joint stock of two partners, whose particular shares differed by 48 dollars, was to the lesser as 14 to 5. Required the shares. Ans. Greater $108, lesser $60. 6. Four men bought an ox for $43, and agreed that those, who had the hind quarters, should pay cent per pound more than those, who had the fore quarters. A and B had the hind quarters, C and D the fore quarters. A's quarter weighed 158 lbs., B's 163 lbs., C's 167 lbs., and D's 165 lbs. What was each per lb., what did each man pay ? and Ans. The hind quarters were $0.06839 per lb., the fore quarters $0.06339. A paid $10.805, B $11.147, C $10.546, D $10.859. 7. A certain person has two silver cups, and only one cover for both. The first cup weighs 12 oz. If the first cup be covered it weighs twice as much as the other cup, but if the second be covered it weighs three times as much as the first. What is the weight of the cover and of the second cup? x= weight of the cover. 12+ weight of first cup covered. Let Then And 6+= weight of second cup, &c. 2 Ans. Cover 20 oz., second cup 16 oz. 8. Some persons agreed to give 6d. each to a waterman for carrying them from London to Gravesend; but with this condition, that for every other person taken in by the way, three pence should be abated in their joint fare. Now the waterman took in three more than a fourth part of the number of the first passengers, in consideration of which he took of them but 5d. each. How many persons were there at first? Let x = the number of passengers at first. Then +3= the number taken in, &c. X Ans. 36 passengers. 9. Four places are situated in the order of the four letters A, B, C, D. The distance from A to D is 134 |