A. 5
B. 6
C. 7
D. 12

Let one of the numbers be “x”; then the other is “x+5”.
Equation:
x + x+5 = 19

2x = 14
x = 7 (the 1st number)
x+5 = 12 (the other number)



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33 Comments to “a number exceeds another number by 5.the sum of the numbers is 19. find the smaller number ?”
  1. Let’s assume that the smaller number is x.According to the problem, the larger number exceeds the smaller number by 5. So the larger number is (x 5).Also, the sum of the numbers is 19.Therefore, we can write an equation as:x (x 5) = 19Simplifying the equation, we get:2x 5 = 19Subtracting 5 from both sides, we get:2x = 14Dividing both sides by 2, we get:x = 7So, the smaller number is 7.

  2. Let’s solve the problem step by step.
    Let’s assume the smaller number is x.
    According to the given information, the larger number exceeds the smaller number by 5. Therefore, the larger number is x + 5.
    The sum of the numbers is 19. So, we can write the equation as:
    x + (x + 5) = 19
    2x + 5 = 19
    2x = 19 – 5
    2x = 14
    x = 14 / 2
    x = 7
    So, the smaller number is 7

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  4. Let’s denote the smaller number as \( x \) and the larger number as \( y \).

    According to the problem:
    – \( y \) exceeds \( x \) by 5, so we have the equation:
    \[
    y = x + 5
    \]

    – The sum of the numbers is 19, so we have another equation:
    \[
    x + y = 19
    \]

    Now substitute \( y = x + 5 \) into the second equation:
    \[
    x + (x + 5) = 19
    \]

    Combine like terms:
    \[
    2x + 5 = 19
    \]

    Subtract 5 from both sides to isolate the term with \( x \):
    \[
    2x = 14
    \]

    Divide both sides by 2 to solve for \( x \):
    \[
    x = \frac{14}{2} = 7
    \]

    So, the smaller number \( x \) is \( \boxed{7} \).

    To find the larger number \( y \):
    \[
    y = x + 5 = 7 + 5 = 12
    \]

    Therefore, the larger number \( y \) is \( \boxed{12} \).

    To verify:
    – The larger number \( y = 12 \) indeed exceeds the smaller number \( x = 7 \) by 5.
    – The sum of \( x \) and \( y \) is \( 7 + 12 = 19 \), which matches the given condition.

    Thus, the solution \( \boxed{7} \) for the smaller number is correct.

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