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.
I don't understand how to do this can you guide me through it and i will take notes.
You understand what consecutive integers are. Now just write down the conditions as algebra:
x + x+1 = 4(x+2)-177
now solve for x.
Sure! I'd be happy to guide you through it step by step.
Step 1: Let's assign variables to the three consecutive integers. We'll call the smallest integer x, the second consecutive integer x + 1, and the largest consecutive integer x + 2.
Step 2: Now, let's translate the given information into an equation. We're told that the sum of the smaller two integers is equal to 177 less than four times the largest integer. In equation form, this can be written as:
x + (x + 1) = 4(x + 2) - 177
Step 3: Simplify the equation by combining like terms. On the left side, we have x + (x + 1) = 2x + 1. On the right side, 4(x + 2) can be expanded to 4x + 8.
So, our equation becomes: 2x + 1 = 4x + 8 - 177
Step 4: Continue simplifying the equation by subtracting 4x from both sides:
2x - 4x + 1 = 8 - 177
Simplifying further:
-2x + 1 = -169
Step 5: Now, let's isolate x by subtracting 1 from both sides:
-2x + 1 - 1 = -169 - 1
Which simplifies to:
-2x = -170
Step 6: Divide both sides of the equation by -2:
-2x / -2 = -170 / -2
The negatives cancel out, leaving us with:
x = 85
So the smallest of the three consecutive integers is 85.
Step 7: To check the answer, we can substitute x = 85 into the equation we formed in step 2:
85 + (85 + 1) = 4(85 + 2) - 177
This simplifies to:
85 + 86 = 4(87) - 177
171 = 348 - 177
171 = 171
Since both sides of the equation are equal, we can conclude that x = 85 is indeed the smallest of the three consecutive integers.
I hope this explanation helps! Let me know if you have any further questions.