GENERAL WRITTEN PROBLEMS 1. A farmer raises 27.5 acres of sugar beets. They average 9.8 T. to the acre. If he sells his beets at $4.40 a T., how much money should he receive? 2. If I lend $2150 for 1 yr. 3 mo. 20 da. at 6%, what amount shall I receive at expiration of time? 3. The floor of a room is 20′ 6′′ long and 14′ 3′′ wide. What is the cost of laying a parquet floor at 24¢ a sq. ft., allowing 10 sq. ft. for projections on the floor? 4. Tell the bank discount and proceeds on a 90-da. note for $2800 discounted at 5% on the day it was made. 5. At a clearance sale, ermine scarfs valued at $155 are reduced to $126.30, and muffs valued at $125 are reduced to $96.25. What is the average per cent of reduction on these two articles? 6. A salesman sold 17 yd. of silk at 89¢ a yd. What is the amount of his sales check? 7. A quart of varnish will cover a space of 150 sq. ft. How much will it cost at $2.80 a gal. to varnish two floors whose dimensions are 18'x15' and 15'x12'? 8. A dealer bought 300 T. of ice for $750. He sold the ice at the rate of 25¢ per cwt. What per cent did he gain? 9. What are discount and proceeds of a 60-day note for $775 discounted 12 da. after date at 5%? 10. What is the amount of these items: 94 lb. cheese @ 15¢ a lb.; 80 oranges at 24¢ a doz.; 7 yd. broadcloth at $1.50 a yd.; 61⁄2 bu. crabapples @ 14¢ per pk.; 7 doz. crackers at $2.50 per gross? 11. A man purchased a house for $5000. The first year he paid for repairs $45, for taxes $75, and for insurance $10. If the house was rented for $40 a mo., what per cent did he gain that year on his original investment? 12. How many cu. yd. of earth will have to be removed in digging a cellar 18' wide, 55' long, and 6 ft. deep? What will the cost be at 60¢ a load of 1 cu. yd.? 13. A note for $2050 dated Jan. 14, 1918 for 4 mo. was discounted Mar. 17, 1918 at 6%. What were the proceeds? 14. A stock clerk earns $14 a week. He pays $6.50 for board, $.70 for carfare, $1.25 for amusement, $.88 for laundry and $3.17 for other expenses. How many weeks I will it take him to save $200? 15. If a dealer buys electric lamps at a discount of 30% and sells them at an advance of 30% on the list price, what rate of profit does he make? 16. A loan of $1260 dated Jan. 2, 1917, was canceled on Dec. 21, 1917 with interest at 5%. What was the amount paid to cancel the debt? 17. Mrs. George H. Hickey has an account with the Fidelity Trust Co. She orders from general store 2 pr. gloves @ $2.25, 31⁄2 yd. silk at $.88 and a hat for $7.65. She receives a discount of 8%. Write out the check for the bill. 18. On Feb. 1, a man's balance was $243.37. Feb. 5, he deposited $181.50, Feb. 10, $60.83 and a check for $27.75, Feb. 13, a check for $75, Feb. 24, $193; Feb. 28, he drew out $370. Find his balance on Mar. 1. 19. Candler Motor Company sells Raymond Hancock an automobile for $1950 less 15% discount, and received his check on the Seaboard National Bank. Write the check. 20. The discount on a note for $500 having 96 days to run is $8. What is the rate of discount? 21. In payment for 300 bbl. of apples at $3.30 a bbl. a dealer wishes to give a 60-da. note, the proceeds of which, when the note is discounted at 6%, will pay for the goods. What is the face of the note? Angles. When two straight lines meet in a point, they form an angle. If one straight line meets another at some point within the second, two angles are formed. If these two lines meet in such a way as to form two equal angles, the lines are said to be perpendicular to each other, and the angles formed are called right angles. If an angle is formed that is less than a right angle, it is called an acute angle. (F A C above.) If an angle is formed that is more than a right angle, it is called an obtuse angle. (D E O above.) Triangles. A figure bounded by three straight lines is called a triangle. The bounding line of a triangle is its perimeter. RIGHT TRIANGLE ISOSCELES TRIANGLE EQUILATERAL TRIANGLE The side upon which the triangle rests is the base. The perpendicular distance from the base to the apex (Note that the altitude is represented in is the altitude. the diagrams by dotted lines.) A triangle containing a right angle is called a rightangled triangle, or a right triangle. A triangle with two of its sides equal in length is called an isosceles triangle. A triangle with all its sides equal in length is called an equilateral triangle. ACUTE TRIANGLE OBTUSE TRIANGLE When a triangle contains only acute angles, it is called an acute triangle. When a triangle contains one obtuse angle, it is called an obtuse triangle. (Note how the altitude is drawn in acute and obtuse ɩriangles.) WRITTEN EXERCISE 1. What is the perimeter of a triangle whose sides measure 9 in., 4 in., and ft.? 2. A park has the shape of an equilateral triangle. A fence enclosing the park is 428 yd. long. How long in feet is the park on each side? 3. Find the perimeter of an isosceles triangle in which the equal sides are 17" long and the other side '. 4. The length of the binding needed for the edge of a triangular kite is 4 yd. If the sides of the kite are all equal how many inches of binding will be needed for each side? Quadrilaterals. A figure that is bounded by four straight sides is called a quadrilateral. This word means "four-sided." When the opposite sides of a quadrilateral are parallel, the figure is called a parallelogram. When the four angles of a parallelogram are all right angles, the figure is called a rectangle. SQUARE When the four sides of a rectangle are all of the same length, the figure is called a square. The base of a figure is the line on which it seems to stand. The height or altitude of a figure is the distance from the base to the highest point, on a line perpendicular to the base. 1. Draw a quadrilateral, the opposite sides not parallel. 2. Draw a parallelogram; a rectangle; a square. 3. Show upon the figures you have drawn in 1 and 2: (a) the altitude; (b) the diagonal. |