find 3 consecutive integers such that the sum of the twice the first and the third is 748.
To find three consecutive integers, we can assign a variable to represent the first integer. Let's call it "x".
The consecutive integer after x would be x + 1, and the consecutive integer after that would be x + 2. So, the three consecutive integers can be represented as x, x + 1, and x + 2.
According to the given information, the sum of twice the first integer (2x) and the third integer (x + 2) is 748.
So, we can set up the equation as follows:
2x + (x + 2) = 748
Now, let's solve the equation to find the value of x:
3x + 2 = 748
Subtracting 2 from both sides:
3x = 746
Dividing both sides by 3:
x = 746 / 3
x ≈ 248.66
Since x represents an integer, we can round it to the nearest whole number:
x ≈ 249
Now that we have the value of x, we can find the three consecutive integers:
First integer: x = 249
Second integer: x + 1 = 249 + 1 = 250
Third integer: x + 2 = 249 + 2 = 251
Therefore, the three consecutive integers are 249, 250, and 251.