And so we represent an odd number as 2 n + 1. It is conventional in algebra to represent an even number as 2 n, where, by calling the variable n, it is understood that n will take whole number values: n = 0, 1, 2, 3, 4, and so on.Īn odd number is 1 more (or 1 less) than an even number. First, an even number is a multiple of 2: 2, 4, 6, 8, and so on. The sum of two consecutive odd numbers is 52. Divide $80 among three people so that the second will have twice as much as the first, and the third will have $5 less than the second.Īnd the third gets $5 less than that, 2 x − 5. The larger number is 10 more: 15.Įxample 6. Then the larger number is 10 more: x + 10. The sum of twice the smaller plus three times the larger, is 55. Then the number after it is x + 1.Įxample 5. Two consecutive numbers are like 8 and 9, or 51 and 52. The sum of two consecutive numbers is 37. The line over x + 12 is a grouping symbol called a vinculum. Then the other number is 12 more, x + 12. In this problem, we are asked to find two numbers. The sum of two numbers is 84, and one of them is 12 more than the other. The whole is equal to the sum of the parts. This is a type of "literal" equation, which is very common in algebra.Įxample 3. The solution here is not a number, because it will depend on the value of b. The problem states that "This" - b - is three more than four times x: (Although b is not known - it is the idea of a definite number - it is not what you are asked to find.) Again, let x represent the unknown number that you are asked to find: Let x be the number of girls. This is three more than four times the number of girls.
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