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9 March, 00:12

The sum of two numbers is 47 and the difference is 19. What are the numbers?

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  1. 9 March, 02:14
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    Answer: The two numbers are 33 and 14

    Step-by-step explanation: We shall start by first assigning letters to unknown variables. Therefore let the two numbers be called a and b. The first clue in this question states that the sum of both a and b equals 47. That means we can write the expression;

    a + b = 47.

    The second clue states that their difference equals 19. This also can be expressed as follows;

    a - b = 19

    Now we have a pair of simultaneous equations which are

    a + b = 47 - - - (1)

    a - b = 19 - -- - (2)

    We shall use the substitution method. Therefore from equation (1), make a the subject of the equation.

    a = 47 - b

    Next we substitute for the value of a in equation (2)

    a - b = 19

    47 - b - b = 19

    47 - 2b = 19

    By collecting like terms we now have 47 - 19 = 2b

    28 = 2b

    Divide both sides of the equation by 2

    14 = b

    We can now substitute for the value of b into equation (1)

    a + b = 47

    a + 14 = 47

    Subtract 14 from both sides of the equation

    a = 33.

    Therefore the two numbers are 33 and 14.
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