Answers to Queries. 197 
algebra. It can, however, be sues as follows :—The part added 
on to the shorter piece of eae is of the longer piece, and =; 
of the remainder—z.e., 7 of = =4. This makes the whole 
ra 
amount added on to be = = Ti es ae = of the ace piece. By the 
ppsHon this = of the long piece is equal tos of the long piece 
and 2 = of 28 ft. or 12 ft. 
Therefore, 16 ft. and = of the long piece is equal to 2 of the 
long piece, from which it pe that 2 of the long piece, less z 
of the long piece (that is, A of the ten piece) is equal to 16 ft. 
The long piece is, therefore, 154 ft. long, and the whole length is 
154 + 28 = 182 ft. J. G. P. VEREKER. 
409.—Another Rule Wanted. 
Remainder = = long and 4 = of this = th of the long part. 
oe = of whole = 28 feet + ir long a5 x 
8 
(2) < = of whole = 28 feet ee i long ges Ok = long part. 
42 + 8 
154 
remainder. 
(3) 3 ~ of whole = 28 feet antl a long (= + a = 
ae, 80 
154 /* 
Multiply by 154; then 66 times whole = 4312 + 50 long. 
But whole = 28 feet + long. 
*, 50 whole = 1400 + 50 long. 
*, 16 whole = 2912. 
Whole = ~? == 113372. 
Or from third line above :— 
Whole = =" and roe ; long. 
_~ = cae and = ° long. 
Also the whole = 28 + long. 
Sue = long = 373. 
Bong 374 x 5 154: 
Total length, 154 + 28 = 182. j.\W. G: 
