the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
a+(a+1)+(a+2)=(a+2)x2 combine like terms
3a+3=2a+4 subtract 2a from both sides
a+3=4 subtract 3 from both sides
a=1 the integers are 1,2,3
To solve this problem, let's use algebra to represent the three consecutive integers.
Let's assume the first integer is x. Since they are consecutive, the second integer will be x + 1, and the third integer will be x + 2.
According to the problem, the sum of these three integers is equal to twice the greatest integer. So we can write the equation:
x + (x + 1) + (x + 2) = 2(x + 2)
Now, let's simplify and solve the equation:
3x + 3 = 2x + 4
3x - 2x = 4 - 3
x = 1
Therefore, the first integer is 1.
The second integer is x + 1, which is 1 + 1 = 2.
The third integer is x + 2, which is 1 + 2 = 3.
Therefore, the three consecutive integers are 1, 2, and 3.