What is the smallest of three consecutive integers if
the sum of the smaller two integers is equal to 177 less than four times the largest?
Note: Consecutive integers are integers that come one after the other. For example: -3, -2 and -1 or 14, 15 and 16. Therefore, if the first number is x, the second is x + 1 and the third is x + 2. Each time we add one to the previous integer to get the next consecutive integer.
smallest number ---- x
middle number ------ x+1
larger number --------x+2
x + x+1 = 4(x+2) - 177
2x+1 = 4x+8-117
-2x = -110
x = 55
See
http://www.jiskha.com/display.cgi?id=1473903464
when you were Madison
PS. by sheer coincidence "helppp's" solution is identical to mine.
To solve this problem, we will use the information given about consecutive integers.
Let's assume the smallest integer is x. According to the definition of consecutive integers, the second integer would be x + 1, and the third integer would be x + 2.
Given that the sum of the smaller two integers is equal to 177 less than four times the largest, we can set up the equation:
x + (x + 1) = 4(x + 2) - 177
Now, let's solve the equation step by step:
Combining like terms, we have:
2x + 1 = 4x + 8 - 177
Simplifying further, we get:
2x + 1 = 4x - 169
Moving the variables to one side of the equation and the constants to the other side:
2x - 4x = -169 - 1
-2x = -170
Dividing both sides by -2 to solve for x:
x = -170 / -2
x = 85
Therefore, the smallest of the three consecutive integers is 85.