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the first day of June, the reading was 477,700. Regarding each cubic foot as 71 gallons, (a) how many gallons of water were used in May ? (b) What was the amount of the bill for water if the price was 124 per thousand gallons, with a discount of 16 per cent?
107. At $1000 an acre, find the value of a strip of land 4 feet by 125 feet.
108. If the specific gravity of iron is 71, how many cubic feet in 1 ton of iron ?
109. A merchant marked goods 25% above the cost; he sold them at 25% below the marked price. What per cent did he lose?
110. The cube of a number divided by the number equals 1764. What is the number?
111. What is the edge of a cube whose entire surface is : 6144 sq. inches?
112. Seven and one half feet are what part of a rod ?
113. Peter has 121% more money than Paul; together they have $6.97. How much money has each?
114. Change the following to a common fraction in its
(a) Interest of $48 for 2 mo. at 6%.
(d) Interest of $330 for 4 mo. at 6%. 116. Answer the following at sight:
(a) Divide 125 by .5.
COOK COUNTY, ILLINOIS. Eighth Grade Examination for County Superintendent's Diploma.
June, 1897. 0. T. Bright, Supt.
Time, 9:30 to 12. 1. What is the ratio of (a) .2% to 2% ? (b) 5 : .5 = ? (c).05 + 5 = ? (d).5 = .05 = ? (e).005 .5 = ? (f).05 • .005 = ?
2. A girl spelled 95% of 60 words. How many words did she miss ?
3. When a vessel sails 160 miles a day, she completes her voyage in 14 days. In what time would she complete it if she sailed 196 miles a day?
4. A three-inch cube was painted on all sides. It was then cut into inch cubes. (a) How many of the inch cubes were painted on three sides ? (b) How many on two sides ? (c) How many on one side ? (d) How many were not painted at all ?
5. Fill the blanks in the following:
A boy had a fish pole 15 feet long. A piece equal to 20% of its length was broken off while catching fish.
(a) The part remaining was — % of the whole pole. (b) The part broken off was — % of the part remaining. (c) The part remaining was — % of the part broken off.
6. The N. E. 1 of the N. W. 1 of a certain section of land was fenced off into four equal fields. (a) What is the shortest length of fence necessary ? (b) How much land in each field ?
7. A straight pole 72 feet high is broken 20 feet from the ground, but is not detached. How far from the foot will the top reach?
(Answer 10 entire questions.)
(b) A man added 18 cows to his herd, thereby increasing the number 25 per cent. How many cows has he now ?
2. If lead pencils that cost 3 cents each are sold for 5 cents each, what is the per cent of profit ?
3. Find the interest on a note for $330 at 6 per cent, given August 3, last year, and due to-day.
4. Write a negotiable, interest-bearing, promissory note. 5. (a) Divide 2 of 5 of 71 by 32.
(b) Subtract 8 from the sum of 51, 25, 47. 6. A rectangular field is 86] rods long and 46.875 rods wide. How much wheat will it produce at the rate of 20 bushels per acre ?
7. A rectangular park, the sides of which are respectively 45 rods and 60 rods long, has a walk crossing it from corner to corner. How long is the walk ?
8. If of 9 bushels of wheat cost $131, what will of a bushel cost ?
9. If hay sells for $14 a ton at a loss of 124 per cent, what must it sell for to gain 15 per cent ?
10. How many pounds of cotton at 74 cents a pound can a broker buy for $9,225, and retain his commission of 21 per cent?
11. Find the proceeds of a 3 months' note for $500 discounted at a bank at 6 per cent.
12. If a building 20 feet high casts a shadow of 6 feet, what length of shadow will a church spire 114 feet high cast?
COOK COUNTY, ILLINOIS.
June, 1898. 0. T. Bright, Supt.
“Mental Arithmetic.” Time, 20 minutes. Fill the blanks :
1. By a sale of goods I lost 121%. The cost was — % of the selling price.
2. The circumference of a 3-in. circle is — % of its radius.
3. A five-inch square is — % greater than a four-inch square.
4. I buy apples four for three cents and sell them three for four cents. I gain — per cent.
5. A and B are 78 miles apart and walk toward each other; A walks 3 miles an hour and B 3,4 miles an hour. When they meet B will have walked — miles.
6. A stick of timber 15 inches square and 32 feet long contains board feet.
7. A horse trots 233 miles in 24 hours. His rate per hour is — miles.
8. $154 was divided among A, B, C, and D, in the proportion of 1, 5, 1, 1 C got — dollars. 9. A school contains 50 pupils :
Monday, 3 were absent in the forenoon,
Friday, all present
10. 64 gal. of wine and 16 gal. of water were mixed. One pint of the mixture contained — of a gal. of water.
COOK COUNTY, ILLINOIS.
Time, 60 minutes. 1. If a quarter section of land has fenced within it the largest possible circular lot, how many acres of the quarter section will remain outside of the circle ? 2. Find the value of the following lumber at $15 per M:
20 pieces 2 x 4, 18 ft. long.
45 16 ft. stock boards, 15 inches wide. 3. (a) What sum invested in 8% bonds at 331% premium will yield an annual income of $1200 ?
(b) What if the bonds were 33} discount ? 4. Find the value of a piece of land 20 ft. x 40 rods at $1000 per acre.
5. What is the ratio of 33 to ő ? Answer in per cent.
New York, January, 1898.
Time, 9:15 a. m. to 12:15 p. m. Answer the first five questions and five of the others, but no more. If more than five of the others are answered only the first five answers will be considered. Give all operations (except mental ones) necessary to find results. Reduce each result to its simplest form and mark it Ans. Each complete answer will receive 10 credits.
1. Define numerator, denominator, divisor, factor, proportion.
2. Find the weight in kilograms of a stone 1 meter square