174 A Treatise of Algebra<2.17 E S T I O N 7 .

One bought 20 Loaves for 16 Pence, whereof some WeftTwo-penny ones, others Penny ones, and the rejl Far*thing ones: What Number of Loaves had he of each fort.

Put x — the Number of the first fort, y = that ofthe second, and z — that of the third ; and, then, bythe Conditions of the Question, we (hall hare these twoEquations,

x 4- y'+ * — r», and8* -f- 4 y -f- z = 64.

Whereof the former being subtracted from the latter, in

order to destroy z, we shall thence get 7* + 37 = 44*

. , 44 — 7* . 2 — *

and consequently y = —-— 14.— 2* 4.- j

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from whence the least Value of and the correspondingValue ofy, in whole Numbers, will appear to be 5 and3 ; and therefore the Numbers fought, equal to 5, 3,and 12 respectively.

QUESTION S.

Twenty Neighbours, in Company together , spent 20 Shit*lings j whereof each Man paid 3 Shillings , each Wo*man 2, and each Child 6 d : How many Men , Womenand Children were they.

By proceeding according to the Tenor of the Ques-tion, we have

*4* 7 4" 2—20, andCx-\- 47 4" 2 — 40.

Let the former of these Equations be taken from the lat-ter, and there will remain $x 4- 37 = 20 j whence 7 =

20 - 5 * 2 — 2X

— — = 6 — a- 4- ; from which, by pro-

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ceeding as above, x will appear to be =1, and 7 = 5:Therefore the Numbers sought are 1, 5 and 14.

Q.U E S T I O N