Three consecutive integers have a sum of 357. Fid the integers algebraically.
I know the three numbers are 118, 119, and 120 but how do you write it in an algebraic expression ?
x + x + 1 + x + 2 = 357
3x + 3 = 357
3x = 357 - 3
3x = 354
x = 118
To find the three consecutive integers algebraically, let's assign a variable to the smallest integer. Let's say the smallest integer is x.
Since the integers are consecutive, the next two integers would be x + 1 (the second integer) and x + 2 (the third integer).
The problem states that the sum of the three consecutive integers is 357. So we can set up the equation:
x + (x + 1) + (x + 2) = 357
Now, we can simplify the equation by combining like terms:
3x + 3 = 357
To isolate the variable, we can subtract 3 from both sides of the equation:
3x = 357 - 3
3x = 354
Finally, we can solve for x by dividing both sides of the equation by 3:
x = 354 / 3
x = 118
So, the smallest integer (x) is equal to 118. Therefore, the three consecutive integers are 118, 119, and 120.
To algebraically represent the three consecutive integers, you can use the variable "x" to represent the first integer.
So, the algebraic expression for the three consecutive integers would be:
x + (x+1) + (x+2) = 357
By solving this equation, you can find the value of "x," which represents the first integer.