Three times the greastest of three consecutive even integers exceeds twice the least by 38. Find the integers.
To find the three consecutive even integers, let's assign variables to represent them. Let's call the first even integer "x", the second even integer "x + 2" (since they are consecutive), and the third even integer "x + 4."
According to the problem, three times the greatest of the three consecutive even integers (which is "x + 4") exceeds twice the least (which is "x") by 38.
So, we can write the equation:
3(x + 4) = 2x + 38
Now, let's solve the equation step by step:
Expand on the left side:
3x + 12 = 2x + 38
Subtract 2x from both sides:
3x - 2x + 12 = 2x - 2x + 38
x + 12 = 38
Subtract 12 from both sides:
x + 12 - 12 = 38 - 12
x = 26
Therefore, the first even integer (x) is 26.
To find the other two consecutive even integers, we add 2 and 4 to the value of x:
First even integer: 26
Second even integer: 26 + 2 = 28
Third even integer: 26 + 4 = 30
So, the three consecutive even integers are 26, 28, and 30.
1st integer = x,
2nd = x + 2,
3rd = x + 4,
3(x + 4) = 2x + 38,
3x + 12 = 2x + 38,
3x - 2x = 38 - 12.
x = 26,
x + 2 = 28.
x + 4 = 30.
The 3 even integers are: 26, 28, and 30.