SUMMARY OF CHAPTER VIII

per cent

66

42. The words

are an abbreviation of “per centum," meaning " by the hundred.” The sign % means per cent. (Sec. 76.)

43. To change a fraction to a per cent, find its decimal equivalent. Then move the decimal point two places to the right and affix the per cent sign. (Sec. 77.)

44. To find the percentage when the base and rate are given, multiply the base by the rate. (Sec. 79.)

45. To find the rate when the base and the percentage are given, divide the percentage by the base. (Sec. 79.)

46. To find the base when the percentage and rate are given, divide the percentage by the rate. (Sec. 79.)

47. To find the cost price when a series of discounts are given, find the amount of the discounts consecutively, subtracting each in its turn. The final result will be the cost price. (Sec. 81.)

48. To figure profit, multiply the estimated cost by the desired rate and add this allowance for profit to the cost. (Sec. 82.)

49. To figure interest, multiply the principal by the rate per annum. If the period stipulated is other than for one year do not fail to take this into account. (Sec. 83.)

PROBLEMS

113. What is 25% of 16? of 48? of 90? of 240? 114. 8 is what per cent of 16? of 40? of 80? 115. 30% off of a number leaves 350. What is the number?

116. A pattern maker allows t" per foot for shrinkage. What per cent does he allow?

117. A contractor figures that 1890 ft. B.M. will be required for the studding in a house. If he add 25% for waste, what

% B.M. must he order?

118. In receiving an order for siding, a contractor gets 650 ft. B.M. in 6' and 8' lengths out of a total of 5000 ft. B.M. What per cent is this?

119. The actual face of a 4" floor board is only 31". What per cent must be added for matching?

120. Maple flooring “ Clear” grade will allow 7% of lengths 2' to 3}' according to the grading rules of the Maple Flooring Manufacturers' Association. How many feet B.M. may be of this length in an order for 74 M.B.M. Clear maple flooring?

121. In laying the floor for a house the contractor allowed 320 ft. B.M. for waste, which was 12% of the total. How many feet B.M. were in the total order?

122. What is the net price of an enameled iron wash bowl if the list price is $18.00 with 30% and 10% off?

123. A contractor figures the actual cost of a job to be $5820. He was awarded the contract at $6550. What per cent of the actual cost was profit?

124. In figuring on a certain job a contractor estimates the actual cost to be $10,490. If he adds 8% for contingencies and 10% of this price for profit, what price will he bid?

125. What is the interest on $500 for 3 years 2 months at 61%

per annum?

126. What will be the total amount of $1200 in 5 years at 5% per year compounded annually?

127. A contractor owns a concrete mixer which cost him $1400. It costs him $15 per day to run the mixer. Figuring money worth 5% and depreciation on the machine at 20%, what will be the total cost of operating the machine per year of 200 days? What will be the cost per day?

CHAPTER IX

RATIO.

PROPORTION. CEMENT AND CONCRETE
MIXTURES. SLOPES. LEVERS.

84. Ratio. We are constantly comparing things with each other. Among many other things we may compare weight, distance or size. In fact, this is exactly what we do whenever we measure the length of a board.

We compare the length of a foot measure with the length of the board and we say that the board is 9 times as long as the foot measure or 9 ft. long. If one plank is 9 ft. long and another is 3 ft. long, we say the first is three times as long as the second or the second is one-third as long as the first. This comparison may also be stated by what we call a ratio. That is, we say the length of the first plank is to the length of the second as 9 is to 3. This is written mathematically, 9:3 org.

85. A Ratio is a Fraction. When the ratio is written in the form of a fraction, it may be reduced to its lowest terms: thus, ==3, which means that the first board is three times as long as the second. Reversing our comparison we have = }, which means that the second board is one-third as long as the first. This ratio is said to be the inverse of the one just preceding. Thus we see that a ratio may be written like a fraction and, like a fraction, it may be reduced to its lowest terms.

Please notice that the things to be compared must be of

=

the same kind. For example, it would be absurd to compare feet with bushels.

A ratio is a mathematical comparison of two things of, the same kind. The two numbers of the ratio are called its terms.

Example. A room is 12' wide and 18' long. What is the ratio of the width to the length?

Explanation. The comparison of the width to the length will be as 12 is to 18. Reduced and expressed as a ratio this is 2 : 3.

86. Cement and Concrete Mixtures. We frequently see the statement that cement mortar is to be mixed in the ratio 1:3. This means that 1 part by volume of cement is to be mixed with 3 parts by volume of sand. A sack of cement weighing 94 pounds contains 1 cu.ft. of cement, very nearly. Thus for every sack of cement we must have 3 cu.ft of sand. Likewise in mixing concrete the directions sometimes state that it shall be mixed 1:21:5 or 1:3:6. Taking the first ratio as an example, this means that the mixture shall be coinposed of 1 part by volume of cement to 22 parts by volume of sand to 5 parts by volume of gravel or broken stone. In order to insure that the mixture shall be uniform and shall completely fulfill the requirements, great care should be taken in measuring and mixing. In Fig. 28 is shown a bottomless measuring box which contains 1 cu.ft. of material for every 3" of height. A box like this, which is 12'' high, will contain 4 cu.ft. Such a box is more accurate and frequently more convenient than the box of an ordinary wheelbarrow for measuring the material.

Example: In making a concrete mixture in the ratio 1:21 : 5 a contractor expects to use 25 sacks of cement. How many cubic feet of sand and gravel does he require?

Explanation. For every sack of cement he will need 21 cu.ft. of sand. For 25 sacks he will need 22 times 25 or 627 cu.ft. of sand. Also for every sack of cement he will need 5 cu.ft. of gravel. For 25 sacks he will need 25 times 5 or 125 cu.ft. of gravel.