Here we will use algebra to find three consecutive integers whose sum is 552.
We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 552. Therefore, you can write the equation as follows:
[tex]X + X + 1 + X + 2 = 552[/tex]
To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:
[tex]X + X + 1 + X + 2 = 552[/tex]
[tex]3X + 3 = 552[/tex]
[tex]3X + 3 - 3 = 552 - 3[/tex]
[tex]3X = 549[/tex]
[tex]\frac{3X}{3} = \frac{549}{3}[/tex]
[tex]X = 183[/tex]
Which means that the first number is 183, the second number is 183+1 and third number is 183+2. Therefore, three consecutive integers that add up to 552 are:
183
184
185
Since, 183 + 184 + 185 = 552, it confirms that the answer above is correct.
