Aryan Y.

asked • 02/04/16# The sum of four consecutive integers is 508. Find the integers.

The sum of four consecutive integers is 508. Find the integers.

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## 3 Answers By Expert Tutors

did you mean to write 506 ?

x+x+1+x+2+x+3=506

4x+6=506

4x=500

x=125

x+1=126

x+2=127

x+3=128

if 506 is correct, here's a shortcut...

506/4=126.5 which is exactly in the middle of the 4 numbers or it's the mean of the numbers

125,126 126.5 127,128

Peggy W. answered • 02/04/16

Tutor

4.4
(15)
The World's Last True Generalist

Aryan:

We only have to translate English to mathematical symbols:

Consecutive integers means that each integer is one greater than the one to the left on the number line. Therefore, we have x, then x+1, the x+2, the x+3. These expressions represent four consecutive integers. Now let's add them. Afterall, we are working with a sum and we know that the sum is 508. The word "is" is replaced with an equal mark.

We only have to translate English to mathematical symbols:

Consecutive integers means that each integer is one greater than the one to the left on the number line. Therefore, we have x, then x+1, the x+2, the x+3. These expressions represent four consecutive integers. Now let's add them. Afterall, we are working with a sum and we know that the sum is 508. The word "is" is replaced with an equal mark.

x + (x+1) + (x+2) + (x +3) = 508

Now simplify the expression on the left. We have 4 of the same variable or 4x. Count them. Our constants (called constants because 1 and 2 and 3 always occupy the same spots on the number lines - constantly. Their values are constant. Their values do not change.) have a sum of 6 (1 + 2 + 3). Now our equation is

4x + 6 = 508

Solve by cancelling the constant (6) first and balancing the equation:

4x + 6 = 508

Solve by cancelling the constant (6) first and balancing the equation:

4x + 6 +(-6) = 508 + (-6)

4x = 502

Now cancel the coefficient (4) and then balance the equation.

1/4(4x) = 1/4(502)

x = 125.5

x + 1 = 126.5

x + 2 = 127.5

x + 3 = 128.5

x = 125.5

x + 1 = 126.5

x + 2 = 127.5

x + 3 = 128.5

The sum of these is 508.

Were you confused with the decimal digits?

Were you confused with the decimal digits?

There's two possible approaches: Algebra, or brute force programming:

Algebra:

A + (A+1) + (A+2) + (A+3) = 508

4A + 6 = 508

4A = 502

A = 125.5 (no whole number solution)

Brute Force Programming (Code in C#, but easily translateable to Java or C++)

for (int A = 0; A < 508; A++)

{

int B = A + 1;

int C = B + 1;

int D = C + 1;

if (A+B+C+D == 508)

{

Console.WriteLine("A=" + A + ",B=" + B + ",C=" + C + ",D=" + D);

}

}

{

int B = A + 1;

int C = B + 1;

int D = C + 1;

if (A+B+C+D == 508)

{

Console.WriteLine("A=" + A + ",B=" + B + ",C=" + C + ",D=" + D);

}

}

No Whole number solution

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Monte G.

02/04/16