10 By a due consideration and application of these Problems, many questions may be solved in a short and easy manner, although some of them are generally supposed to belong to higher rules.] PROBLEM 1. Having the sum of two numbers, and one of them given, to find the other. Rule. Subtract the given number from the given sum, and the remainder will be the sum required. Let 288 be the sum of two numbers, one of which is 115, the other is required. From 288 the sum, Take 115 the given number. Remains 173 the other. PROB. 2. Having the greater of two numbers, and the differonce between that and the less given, to find the less. Rule. Subtract the one from the other. Let the greater number be 325, and the difference between that and the other 198: What is the other? From 325 the greater, Remainder 127 the less. PROB. 3. Having the lesser of two numbers given, and the difference between that and a greater, to find the greater. PROB. 4. Having the sum and difference of two numbers given, to find those numbers. Rule. To half the sum add half the difference, and the sum is the greater; and from half the sum take half the difference, and the remainder is the less.-Or, from the sum take the difference, and half the remainder is the least; to the least add the given difference, and the sum is the greatest. What are those two numbers, whose sum is 48, and difference 14? 2)48 Half sum =24 2)14 Half diff. 7 24+7=31 the greater; and 24-7-17 the less. Or, 48-14-2=17; and 17+14=31. PROB. 5. Having the sum of two numbers and the difference of their squares* given, to find those numbers. Rule. Divide the difference of their squares by the sum of the * numbers, and the quotient will be their difference: You will then have their sum and difference, to find the numbers by Problem 4. What two numbers are those, whose sum is 32, and the difference of whose squares is 256 ? 32)256(8 difference. Half sum 16 4 Greater 20 Less 12 PROB. 6. Having the difference of two numbers, and the dif ference of their squares given, to find those numbers. * The square of a number is the product of it multiplied into itself. H |