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LESSON 2. The yearly interest of a sum at 6 per cent. is equal to so part of the principal added to 250 dollars; what is the principal?
Ans. $ 25000. Suppose the principal to be 500 dollars. Rate per. cent.
6 Interest for 1 year,
30|00 to of 500=
25 Excess only,
5 dollars. Here the excess over to is only five dollars interest instead of 250. Now
say, if 5 excess of interest, arises from 500 principal; what did 250 excess arise from?
5 : 500 :: 250 to a fourth number.
5)125000 Ans. 25000
LESSON 3. Of a certain sum lent, I received one fourth, one fifth, and one sixth, which amounted to 185 dollars; what was the sum lent?
Answer, 300 dollars.
Suppose I lent 60 dollars.
37 : 60 :: 185 15
111 Result, 37
...00 LESSON 4. A and B have a salary each alike for 3 years ; A saves of his wages, but B spends the whole of his and one third nore, falls in debt fifty dollars yearly, and at the end of 3 years, after settling his accounts, has only 20 dollars left of a present given by his uncle at the commencement of business; what was the salary? And how much the preRent ?
Answer, the salary was 150 dols. each.
The present was 170 dollars to B.
OPERATION. Suppose the salary to be 6 dols. Result. Pos. Result. The third of 6 =
6 :: 50 B spends 50 dollars a year
50 more than his salary for 3 years = 150 dol. and 20 he
2)300(150 Sal. had left = 170 the present.
LESSON 5. On the 25th day of October 1815, while penning this lesson, I find that one fifth of the years I have lived, multiplied by 6, and the fourth of my years added to that product, make 87; what is my age? Answer, 60 years.
R. Position. R. } of 80 = 16
shall be yours.
6 Says George to Harry, I have a sum of money to buy books; the and } a ţ of which will make 4 dollars and 50 cents; if you will tell me how much I have, 2 dollars
Answer, 9 dollars. Suppose 12 dollars.
R. P. R. The of 12 = 4
6 : 12 4.50 The 4 of 4 2
12 Result, .6
6)54,00 Answer, 9.00
· DOUBLE POSITION, Is when we use two suppositions : and if we miss in both, observe the nature of the errors and work accordingly. When the errors are both less, or both greater than the given number, they are alike; but if one be greater and the other less than the given number, they are unlike.
RULES. 1. When the errors are alike, take their difference for a divisor, and the difference of their products for a dividend.
2. When the errors are unlikc, take their sum for a divisor and the sum of their products for a dividend.
LESSON 7. A B and C would divide 250 dollars between them in such manner that B. may have 7 dols. 50 cents more than A, rand C 10 dols. more than B; how much must each man have? Answer, A must have 75 dols. B, 82.50 and C,92.50.
OPERATION. 1st. Suppose A, 20
2nd. Suppose A, 40 B, 27.50
B, 47.50 C, 37.50
85.00 Given number, 250.
Result, 145.00 Given number, 250.
2nd. Error, 105
Having proceeded according to the proportions mentioned in the question, and placed the suppositions and errors as here represented, multiply them crosswise, that is, multiply the first error by the last sụpposition, and the last error by the first supposition. Supposi. Error.
165 1st. 20 165
40 2nd. 40 105
1st product, 6600 First error, 165
105 Second, 105 First supposi.
20 Difference, .60 for a divisor. 2nd Product, 2100 First product, 6600
610)4500 Second, 2100
75. Dividend, 4500
LESSON 8. 6 A saddle is worth 50 dollars : two horses are of different value: when the saddle is on the first horse it raises bis value to double the second; but when it is on the second horse, his value is triple the first: What is the value of each horse?
Ans. The price of the first horse is 30 dollars, and the second 40.”
OPERATION. 1st. Suppose the first horse worth,
38 dol. The saddle,
Their combined value,
Their combined value,
94 Three times the value of the first horse 38x3=114
The difference between 114 and 94 is the
2nd. Suppose the first horse worth,
Their combined value,
The difference between 126 and 96 is the
30 first horse.
50 saddle. First product, 1140.
80 saddle and horse.
Diff. or divisor, 10
LESSON 9. “ A boy stealing apples being taken by mad Tom, gave over half he had stolen, and Tom gave him back 10; in his return home, he was met by raving Ned, who took from him one half of what he had left, and returned him back 4; after that, unluckily, positive Jack meets him, and takes away one half the remainder, giving back 1; at last getting safe away, he finds he has 18 left: How
had the boy at first?