All To find the perimeter, given a. one side of any equilateral figure. A4 B4 D1 E5 G1 C1 b. two adjacent sides of a rectangle or parallelogram. A5 B11 C6 D10 E3 c. the diameter or radius of a circle. G5 H4 18 J1 53 G13 H6 124 J7 144 b. 1. the three dimensions of a rectangular solid, such as room, bin, wood pile, etc. A10 B3 C8 D15 E6 F5 G9 H37 118 J11 122 c. the altitude and diameter or radius of a cylinder. HI 17 15 15% 25 e. the area of the base of a prism or cylinder and its altitude. f. the area of the base of a pyramid or cone, and its altitude. A1 C1 E1 ΕΙ F4 G12 11 A13 To find a difference, given denominate numbers of different denominations. C1 A14 To find the average given a series of items. (To find the average, given the total amount and the number of items is classified as A4.) A7 B1 C7 D3 E6 F3 G5 H31 13 J13 79 A15 To find the ratio of one number to another, given the two numbers. A73 B52 C41 D116 E125 F80 G66 H264 153 J54 924 A16 To find a part of a number, given the ratio of the part to the number and the number. (The fraction may be in terms of fractions or decimals.) A69 B83 C18 D125 E45 F28 G64 H78 I114 J52 676 A17 To find a number, given a part of it and the ratio of that part to the whole. A18 To divide a quantity into parts having a given ratio, given the quantity and the ratio. A12 B7 C5 D2 H28 113 J10 77 97 A19 To find a member of a ratio, given two members of one ratio and one member of another ratio equal to the first. (Inverse ratio included.) A49 B181 C76 D116 A20 To find the ratio of items to total, given a series of items. E14 G3 H40 15 J6 73 117 B1 A21 To compare pairs of quantities by ratios, given the pairs of quantities. A1 C5 C20 ᎠᏎ E15 F1 G11. H46 17 J12 A22 To find the largest quantity which will be contained equally in two or more given quantities. B7 7 7 A23 To find the least quantity which will contain exactly each of two or more quantities. B9 A24 To draw to scale, or to represent graphically in tables. A8 B14 C39 D42 E23 F31 A12 B22 C68 D60 E27 F33 A25 To interpret tables, graphs, or diagrams, given completed graphs, tables, or diagrams. J7 293 A26 B19 C61 D23 E30 F26 G12 H82 17 B. ACTIVITY PROBLEMS B1 Buying and selling,' simple cases. a. To find the total price:2 1. given the number of units and price3 per unit. 349 A67 B92 C51 D206 E90 F29 G107 H179 1212 J162 1195 D3 E8 A25 B3 C1 D7 E8 b. To find the number of units: 130 1. given the total price and price per unit. 'Descriptions of quantitative relations given below are expressed in terms of buying. In some cases changes in terminology would be necessary if the activity were to be considered from the standpoint of selling. "Total price" is used to designate the amount received for several units of the same commodity rather than the amount received for several commodities. "Price" is used to designate the quantity taken as a basis of computation. Usually "price" refers to the value or worth of a unit rather than a specified number of units. "Price" is often limited by the qualifying terms cost, selling, marked, and list. 2. given the total price and the price per unit in another denomination. 1 1 3. received in exchange of commodities, given an amount of each commodity and the unit for each. C2 22 2 4. given the price per unit of each of two commodities, the total price of both, and the ratio of the number of units of one to the number of units of the other. 2 7 2. given the total price and the number of units in another denomination. A1 A3 G1 F1 G2 J1 3. in exchange of commodities, given the number of units of each commodity and the price per unit of one. B2 B2 22 4. given the number of units of each, the combined price of both, and the ratio of the price of the one to that of the other. 1. To find the amount to be received for several items, given the price of each. A7 B3 C3 D4 E19 F8 G3 H13 11 J3 64 A22 B22 C15 D37 E72 F43 G28 H28 112 J51 330 . To make change, given an amount of money and the price of a commodity. A1 B1 1. given the number of units and the margin or loss per unit. 2. given the unit cost, the unit selling price, and number of units. A1 B10 C1 D2 E3 F1 G5 C1 D2 E6 F1 G6 H2 13 J9 To find the margin or loss per unit, given the total margin or loss and the number of units. D1 A2 B1 C3 D30 E2 F3 G1 H13 1 55 55 [argin is a term used to represent the difference between the cost price and the price and therefore is a substitute for the words "gain" and "profit" as they nmonly used. B2 Buying and selling, more complex types. a. To find the selling price: 1. given the rate of discount or loss, and the price. 141 J14 521 162 J35 667 F6 G8 H25 18 J5 93 194 162 206 4. given the price, rate of advance or margin, and rate of discount or loss. A2 B2 5. given the rate of commission, discount, margin, or loss and the amount of commission, discount, margin, or loss. 6. given the price and the amount of commission or discount. E2 A6 B18 C9 D14 F4 F4 G9 H5 11 J11 b. To find the amount of margin, loss, commission or discount: 1. given the total price and the rate of margin, loss, commission or discount. A49 B26 C5 D104 E6 F16 G29 H34 19 J10 288 A91 B76 C30 D140 E28 F30 G53 H70 125 J50 593 2. given two or more successive discounts and the total price. c. To find the rate of margin, loss, discount, advance or commission: 1 3 1. given the total price and the amount of margin, loss, discount, advance or commission. A65 B11 C8 D2 E14 F17 G3 HI 12 J5 128 A122 B78 C63 D93 E30 F36 G30 H14 123 J60 549 2. given the cost price in terms of two successive rates of discounts and the list price, and the selling price in terms of a single rate of discount and the list price. 1. given the selling price and the rate of discount or loss. 2. given the amount of margin, loss, commission, or discount and the rate of margin, loss, commission, or discount. 'Rate may be expressed in terms of percent or as a fraction. 4. given the selling price and two or more successive discounts. e. To find the amount due the agent or agents, given the number of units, the price per unit, and the rate of commission. (Agent purchases commodity.) f. To find the equivalent single discount in percent, given two or more successive rates of discount. C1 E1 22 2 2 g. To find one of two or more successive discounts, given the list price, one or more of the successive discounts in percent, and the net price. B3 Carrying on a business. 1 1 Note: Types listed under "carrying on a business" are similar in certain respects to those found under the activity of "buying and selling," but in general the following distinction prevails. The problems under B1 and B2 are those in which a purchaser is explicitly involved and in which he may be expected to be interested, at least to the extent of checking the solution by the seller. The problems under B3 are those which in general only the one carrying on the business will encounter. The degree of magnitude of the quantities of the problem and the terminology were also used as criteria. In cases where the distinction is not obvious, a footnote indicates similarities or differences. a. To find the selling price: 1. (a) given the cost price, rate of net profit, and rate of overhead. (Profit and overhead are figured on the cost price.) (b) given the cost price, rate of net profit, and rate of overhead. (Profit and overhead are figured on selling price.) 2. (a) given the cost price, rate of net profit, and the overhead. (Profit is figured on cost.) (b) given the cost price, rate of net profit, and the overhead. (Profit is figured on selling price.) b. To find the total receipts, given the total cost and the net profit. E1 3 1 c. To find the overhead, given the cost price or selling price and the percent of overhead. d. To find the rate of overhead, given the cost price or selling price and the overhead. General terminology and "overhead" are the factors which distinguish this classification from B2a. |