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3 November, 08:41

Find three consecutive odd integers such that the sum of the largest and twice the smallest is 25. If x represents the smallest integer, then which equation could be used to solve the problem?

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Answers (2)
  1. 3 November, 10:54
    0
    The three integers are 7, 9, 11.

    The equation is: 2x + x + 4 = 25

    Step-by-step explanation:

    The problem asks to use x to represent the smallest of the three integers.

    Odd integers are 2 units apart, such as 1, 3, 5, 7. The difference between consecutive odd integers is 2.

    Since the smallest odd integer is x, then the next larger one is x + 2. The largest odd integer is x + 2 + 2, or x + 4.

    The three odd integers are

    x, x + 2, x + 4

    The problem then states "the sum of the largest and twice the smallest is 25."

    The largest one is x + 4.

    Twice the smallest is 2x.

    Their sum is 2x + x + 4.

    That sum equals 25.

    2x + x + 4 = 25

    3x + 4 = 25

    3x = 21

    x = 7

    The smallest integer is 7.

    Then x + 2 = 7 + 2 = 9,

    and x + 4 = 7 + 4 = 11.

    Answer: The three integers are 7, 9, 11.

    The equation is: 2x + x + 4 = 25
  2. 3 November, 12:23
    0
    The three consecutive odd integers : 7, 9, 11

    Further explanation

    Algebraic expressions in mathematics are a combination of coefficients, numbers, variables, constants and arithmetic operations such as addition, subtraction, multiplication, and division.

    The main composition of algebraic expressions are:

    • 1. phrases

    algebraic forms separated by arithmetic operations

    consists of one phrase (monomial) to many phrases (polynomial)

    • 2. variable

    is a value that can be changed, can be in the form of letters, for example, x, y, a, b, etc.

    • 3. constants

    is a fixed value, can be a number

    • 4. arithmetic operations

    +, -, :, x

    integer number: numbers consist of positive, negative and 0 numbers

    Odd number: Any integer that cannot be divided by 2.

    The last digit is 1, 3, 5, 7 or 9

    Because it is divided by 2, the difference between the two numbers is also 2 for consecutive numbers

    Then consecutive odd numbers can be symbolized:

    x, x + 2, x + 4, x + 6, x + 8, etc.

    For example, 3 consecutive odd numbers are:

    x + 4, x + 6, x + 8

    the sum of the largest and twice the smallest is 25, can be expressed in terms of arithmetic operations:

    (x + 8) + 2 (x + 4) = 25

    So the solution:

    x + 8 + 2x + 8 = 25

    3x + 16 = 25

    3x = 9

    x = 3

    So the smallest number is:

    = x + 4

    = 3 + 4

    = 7

    or

    Find three consecutive odd integers such that the sum of the largest and twice the smallest is 25. If x represents the smallest integer, then which equation could be used to solve the problem? 2x + x + 2 = 25 2x + x + 4 = 25 2x + 2x + 4 = 25.
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