Three consecutive integers are such that the sum of the largest number and 2 times the middle number is 27 more than twice the smaller number
If x is the smallest, then
(x+2) + 2(x+1) = 27+2x
To solve this problem, let's represent the three consecutive integers as x, x+1, and x+2.
According to the problem, "the sum of the largest number and 2 times the middle number is 27 more than twice the smaller number." We can express this as an equation:
(x+2) + 2(x+1) = 2x + 27
Let's solve this equation step by step:
1. Distribute the 2 to (x+1):
x + 2 + 2x + 2 = 2x + 27
2. Combine like terms:
3x + 4 = 2x + 27
3. Subtract 2x from both sides:
3x + 4 - 2x = 2x + 27 - 2x
x + 4 = 27
4. Subtract 4 from both sides:
x + 4 - 4 = 27 - 4
x = 23
Therefore, the consecutive integers are 23, 24, and 25.