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2. Proof of Example 1.--1f 48 dollars will pay for 12 yards of cloth, how many yards can be bought for 16 dollars ?
$ yds. $ 48 : 12::16
w In this question the answer 12
must be yards; therefore, we write
12 yards for the second term. As 48)1924 yds. Ans. 16 dollars will pay for a less num. 192
ber of yards than 48 dollars, we
write 16 dollars on the right of the 12 yards for the third term, and 48 dollars on the left for the first term.
3. If 6 yds, of cloth cost $10, what will 20 yds. come to?
yds. As 5 : 10 :: 20
Here we divide the 2d term by the 1st, and multiply the quotient into the 31, for the answer.
yds. $ yds. As 5 : 10 :: 20
$40 Ans. Here we divide the 3d term by the 1st, and multiply the into the 2d, for the answer.
4. If 20 yds. cost $120, how many yards may be bought for $30
$ yds. $
As 120 : 20 :: 30 120---20=6 quot. and 30---6=5 yards, Answer. Here we divide the 1st term by the 2d, and then, the 3d term £ ihe quotient for the answer.
$ Again, As 120 : 20 : : 30
120;30=4 quot. ani, 20-4=5 yards, Ans. Here we divide the 1st term by the 3d, and then, the 2d term by that quotient for the answer.
6. If i cwt of tobacco cost £5 128. 91d. what will 8 cwt. do. cost?
Cwt. £ s. d. Cwt.
Ans. £45 24 Here there is no need of reducing the middle term, because it can be performed by compound multiplication, the first term being an unit.
6. If 8 cwt. of tobacco cost £45 2$. 4d. ; what is that per cwt ?
£ $. d. 8)45 2.4
Ans. 5 12 9 Here there is no need of reducing the middle term, because it may be performed by compound division only, the 3d term being an upit.
7. If 2 cwt 1 qr. 14 lbs. of sugar be worth $21.75, what will be the value of 42 cwt. 3 qrs. at the same rute ? Cwt. gr. lb. $ c. 2 1 14 : 21.75 :: 42 3 4
W lo this example, the
first and third terms are com1368
pound numbers, therefore, we 342
reduce them both to the least
denomination mentioned in ei4788 lbs. ther, viz. pounds. The se2175
cond term is reduced to the
least denomination mentioned 23940
in it, by calling it all cents. 33516
We then multiply the third 4788
term by the second, and divide. 9576
the product by the first term,
$ C. and the quotient is 39150 cents, 266)10413900(391.50 A. which we reduce to dollars by 798
pointing off the two right
hand figures. 2433 2394
8. If 9 cwt. 3 qrs. of sugar cost £27 178. 6d., what will 2 cwt. 1gr. 1 lb. cost?
£ s. d.
Cwt. gr. lb.
2 1 1
Here it will be seen, that the first and third terms are of the same kind, but of different denominatious, and therefore are reduced to the same name or denomination, and that the demand of the ques. tion lies on the 3d term.
2. That the middle term, being given in pounds, shillings and pence, is reduced to pence. But
3. If the second term were in federal money it would be sufficient to proceed according to decimals.
9. If my income be 109 güideas per aonum, k desire to know what may spend per day, so that I may lay up £45 at the year's end ?
Ang. £o 59. 104d. ts per day.
NOTE 1.-You must subtract £45 from the value of 109 guineas.
%. There being 365 days in a year, your question must next be stated thus ;
D. Guin. £
10. If my salary be £43 12s. 5d. per annum, what does it amount to per week ?
Ans. £0 16s. 9374. The Stating
NOTE. As there are 52 weeks £ s. d. W.
and 1 day in a year, you will get As 52 : 43 12 5 ::1: the Aas. the true answer to tbe above ques
tion by the following ratio.
11. Suppose my income to be 16. 830 d. per week, what is it per
Ans. £43 13s. 77 d.
Note 1.-You must first reduce the middle term to pence. 2. You must multiply by 365 (the denominator of the fraction) and add to the prodact the 283 which remains; and remember always 10 do so in similar cases.
3. You must divide by 7, the first term, and the quotient will be the answer in 365ths of a penny, which (in all similar cases) must be first divided by the denominator, and then brought into pounds.
12. How many yards of cloth may be bought for $195 750. of which 94 yds. cost $i1 2c. ?
Abs. 168 yds. 3 qrs.
13. A merchant, failing in trade, owes in all £3475, and has în money and effects but £2316 139. 4d.: Now, supposing his effects are delivered up, pray, what will each creditor receive on the pound? £ £
14. If the distance from Newburyport to York be 31 miles ; I demand how many times a wheel, whose circumference is 154 feet, will turn round in performing the journey ?
Ans. 10560 times.
15. What will 371 gross of buttons come to at 13 cents per dozen ?
Aps. $58 50c.
16. If 7 of a ship cost $1163 what is the whole worth?
Ans. $2658 28c. 5m.
17. A merchant bought 9 packages of cloth, at 3 guineas for ? yards; each package contained 8 parcels, each parcel 12 pieces, and each picce 20 yards; how many dollars came the whole to, and how many per yard ?
yds. guin. pack. $
yds. guin. yd. $
18. A merchant bought 49 tuns of wine for $910; freight cost $90; duties $40 ; cellar $31 67c.; other charges $50, and he would gain $185 by the bargain ; what must I give him for 23 tups ?
$ $ $ Tuns. $ As-49 : 910+90+40+31 67+50+185 : : 23 : 613 33c. Ans.
19. The earth being 360 degrees in circumference, turns round on its axis in 24 hours ; how far does it turn in one minute, in the 43d parallel of latitude; the degree of longitude, in this latitude, being about 51 statute miles ?
D. M. M. M.
20. If a staff, 4 feet long, cast a shade (on level ground) 7 feet, what is the height of that steeple, whose shade, at the same time measures 198 feet ?*
F. sh. F. hei. F. sh. F. hei.
* As the rays of light from the sun may be considered parallel, the length of the sbadows must be proportioned to the heights of the objects. Hence the reason of the statement of this question.