using n as the variable, how do you find 3 consecutive integers in which 3 times the sum of the first two is 16 more than the third?
To find three consecutive integers that satisfy the given condition, let's proceed step by step:
Let's assume that n represents the first integer.
The second consecutive integer would be n + 1, and the third consecutive integer would be n + 2.
According to the given condition, "3 times the sum of the first two is 16 more than the third." In terms of a mathematical expression, this translates to:
3(n + (n + 1)) = (n + 2) + 16
Now, we can solve the equation to find the value of n:
3(2n + 1) = n + 18
Simplifying further:
6n + 3 = n + 18
Subtracting n from both sides:
6n + 3 - n = 18
5n + 3 = 18
Subtracting 3 from both sides:
5n = 15
Dividing both sides by 5:
n = 3
Therefore, the first consecutive integer is 3, the second is 4, and the third is 5.
Hence, the three consecutive integers that satisfy the given condition are 3, 4, and 5.