Education > Complete treatise on practical arithmetic and book-keeping

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S. To find two numbers, of whieb the sum is 16 an4
their product 63. Ans, 9 and 7. $
From the square of £ the sum subtract the product, and Jj
the square root of the remaindw is | their difference, which
added to \ the sum gives the greater.
4. To find a mean proportional between 28 and 7.
Ans. 14. | ;J
Take the square root of their product.
5. To find two mean proportionals between 12 and 324.?
Divide the greater by the lesser; the cube root of thej
quotient is the ratio ; by which multiply the lesser to get v.
the lesser mean ; and the lesser mean by it to get the greater, f.
6. The number of horned cattle on a farm is a mean pro- }
portional between the numbers of the horses and the sheep;!
the sum of the three nlimbers is 258, and their product* «■
4 6656 : How many are there of each ?
Ans. 6 horses, 36 cattle, and 216 sheep, i
The cube root of 46656 is the cattle, and the square off ,
the cattle is the product of the horse and sheep, which may]
be found by the third example.
7. To divide the number 23 into extreme and mean ratio; j
that is, so that 23 shall be t<? the greater part as the greater! ''
to the less.
From the square root of 5 subtract 1 ; the remainder mul-j *
tiplied by | the number gives the greater part.
8. After dealing a hand of cards to each in company,, ,
there remained 25 cards in the paclc ; and after giving one? i
more to each, there remained 4 hands in the pack : Howj v
many were there in company, and how many cards were ! ,
dealt to eachuat first i Ans. 9 in comp. 3 cards each. | .
The pack consists of 52 cards, and there had been dealt j
27 cards at firsf: Find two numbers, as in the 3d example,' 1
of which the sum shall be 25— 4=: 21 > 3.ud their product j
27 X 4=: 108 ; and the lesser of the two is the number iq |
company, and i of the greater is the cards in a hand,
9. To fiqd two numbers, of which the sum shall be 21, j
and the sum of their squares 225. Ans. 12 and 9. j
From the square of the sum subtract the sum of their
squares, and % the remainder is their product; from which
the numbers may be found as in the 3d example.
10. There were 800 trees planted in ap oblong form, and