Elementary arithmetic, with brief notices of its history... by Robert Potts.

35
tained in the former, when both sums are expressed in the same units. 9. The
difference is contained 4-2 times i times he sum. 10. 4- of 1 guinea is equal to Is. 7 -d.
11. 998 _7ii4, an abstract number denoting the number of times the less sum is contained in the greater.
12. Here 17s. 6d. is equivalent to 840 farthings, and 25 new to 24 old farthings,
and 1 new is 24 of one old farthing: 840 new = 2iX 840 = 8062- old farthiIlgs.
840-8062=333 old farthings loss per week. And 33XX52=1747- farthings-=
~1 1Gs. 4-d. loss yearly.
XVI.
1. ~34 8s. 4ld. 2. ~1 gives Is. 2d. - of ~1: ~100 gives ~-, or 5- per
cent. 3. First one halfpenny is the gain on three halfpence, the gain is ~ of the
capital, and the gain on ~100 is ~33 —, or 13~ per cent.
Secondly, one halfpenny is the gain on four halfpence, the gain is - of the capital,
and the gain on ~100 is ~25, or 25 per cent. The difference is 8A per cent.
4. ~100 bequeathed gives ~90 to legatee, or he receives ~90 for 100 bequeathed,
and ~1 for ~o~, and therefore, ~1000 for 1~000, or ~1111- the sum to be bequeathed.
5. First prime cost 3s. 6d. or ~-x gives 4~d. gain: ~1 gives Us. gain, and
15X 100
~100 gives X 2- or ~10~ gain, or 10~- per cent.
Secondly, 3s. lOdc., or ~1,-, gives 4~d. loss, and ~1 gives ~Os. loss, andc therefore
100X60 _
~100 gives 3X- X or ~9~ los or or 9 per cent.
6. 33- per cent. 7. 27 of ~1. 8. Neither gain nor loss. 9. With ~4~ gain,
the prime cost is 100, and ~4-, is contained a1- times in ~47 14s. Hence ~47 14s.
ives X 100=~530, the prime cost. 10. 21 s. 11. 2s. 112 d. 12. 10-s.
raives 215
12. Let 1 denote wholesale price to the retailer, who makes a profit of 25 per
cent.
25 1 o
Then 1+- 1 + 1 or 5 =16s.
100 4 4
therefore 1 = 6412s.
5
Next, let 1 denote the manufacturer's price to the wholesale dealer, who makes
a profit of 15 per cent,
15 3 23
Then 1+ =1+- or 2=124s.
100 20 20
256
therefore 1 =256=1s.
23
Thirdly, let 1 denote the original cost of the article to the manufacturer, who
mnakes a profit of 10 per cent.
10 I 11
Then I+- =1~- or 11 1-s.
100 10 10
256 10 2560
therefore 1 =2 X 1 _256 105 —s.
23 11 253 252
Or the cost to the manufacturer is 10-53s.
XVII.
1. A franc, 10d. = s. =~ I=- 2 of 1 guinea. 2. 1 guinea=504-6=498 halfpence: and 1 franc=19 halfpence. As 498 and 19 are prime to each other. The
L.C.LM. =19 x 498. Hence 19 sovereigns, or 498 francs, are the least numbers of
these coins that can be exchanged. 3. 25714' francs. 4. 8571 l rupees. 5.
10 scudi = 52I francs, and 1 scudi= 21 of 1 franc.; 20 francs =16s., and 1 franc =4 of