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

38
XXVI.
1. 3661 cubic feet. 2. 1728 cubes. 3. 320 cubes. 4. 6 feet long. 5 16 yards.
6. 633600 cubic yards. 7. 334~~4 cubic feet. 8. 2~- feet long. 9. 960 feet long.
10. 32 feet deep. 11. 7,800 bricks. 12. The content of the chest is 5644 cubic feetQuantity of wood used 81 cubic feet. Difference between the external and internal
surfaces of the chest 8$ square feet.
XXVII.
1. 19801bs. 2. 8190lbs. 3. The weight of a cubic foot of the stone is 160lbs,
The weight of the block 235,9501bs. 4. Supposing the internal dimensions given,
the external dimensions will be 10ft. llin., 8ft. 7in., and 5ft. l1in. The vessel
consists of 35Oy~-54- cubic feet of iron, of which 4 cubic inches weigh one pound Avoirdupois. 5. The internal surface of the cistern is 14349 square feet, and 17"4'' cubi>
feet of lead are required to line it. 6. 1 yard of wire requires g-. of Ilb. of copper,
and 50 miles require 4,000lbs. The area of a section of the wire can be found by
dividing the number of cubic inches of copper in the wire by its length. 7. 384 feet.
8. 761744 square yards. 9. 275625 leaves.
XXVIII.
1. Since six men earn ~7 6s. 3d. in 7-2 days, they earn 19s. 6d. in one day, and.
one man earns 3s. 6d. in one day. The 10 men will earn ~1 15s. in one day, and iii
11- days they will earn ~20 11s. 3d. 2. Take an hour as the unit of time.
3. Here 3 men and 5 boys in 4 weeks earn ~11:
therefore 3 men and 5 boys in 1 week earn ~24,
and 6 mene and 10 boys in 1 week earn ~51-.
But 7 men and 10 boys in 1 week earn ~06:
therefore 1 man in 1 week earns ~-,
and 3 men in 1 weelc earn ~1X!.
Whence 5 boys in 1 week earn ~14,
and 1 boy in 1 week earns ~X.
Wherefore 5 men and 4 boys earn in 1 week ~32.
But 5 men and 4 boys earn in some number of weeks, ~14.
The time required is 14.-3~=4 weeks.
4. 18 days. 5. Let the work of one child be taken as the unit. Then the worik
of 9 men, 11 women, and 9 children is equivalent to the work of 71 children. Themen receive ~1 14s. 4~d., the women ~1 5s. 2~d., and the children 5s. 6d.
6. Let the wages of 1 child be taken as the unit.
AVages of 1 man and one child are equivalent to the wages of 4 womlen.
Wages of 1 manl and 3 children are equivalent to the wages of 5 women.
Hence the wages of 2 children are equivalent to the wages of 1 woman,
and the wages of 1 man is equivalent to the wages of 3~ women or 7 children.
Therefore the wages of 1 man, 1 woman, and 3 children, are equivalent to the sum of
the wages of 7 children, 2 children, and 3 children, or 12 children.
But the amount of these wages of 12 children is 30s.
The man's wages are 17s. 6d., the woman's 5s., the 3 children 2s. 6d. each.
7. ~350 for 7 weeks' work gives ~50 weekly. 2 men or three women receive as
much as 5 children, therefore 1 man receives as much as 2 children, and 1 woman as.
4 children. And 20 men receive as much as 50 children, 40 women as 662 children,
and consequently 20 men, 40 women, and 50 children receive together as much as
1664 children in 1 week. Each child receives ~50- 166-= 6s. weekly. 1 woman.
3 X6=10s., and 1 man 4X6=15s.
XXIX.
1. Here 1 man performs I-oeo- of the work in 1 day, and a certain number of men
perform 2 in one day. Hence 5* — '-o1200, the number of men.
5 ~ ~~~~~~~ ~-UO ' —