Three consecutive integers are such that four times the least integer is three times the greatest. what is the greatest of these three integers?
let the 3 consecutive integers be x-1, x, and x+1
4(x-1) = 3(x+1)
4x - 4 = 3x + 3
x = 7
Your 3 integers are 6, 7, and 8
To find the greatest of these three consecutive integers, we can break down the given information step by step.
Let's assume the three consecutive integers are x, x+1, and x+2.
According to the given information, "four times the least integer is three times the greatest." This can be represented as:
4 * x = 3 * (x+2)
Now, let's solve this equation to find the value of x:
4x = 3x + 6 (using the distributive property on the right side)
4x - 3x = 6 (subtracting 3x from both sides)
x = 6
So, the smallest integer is 6.
To find the greatest integer, we can substitute the value of x back into our initial assumption:
x + 2 = 6 + 2 = 8
Therefore, the greatest of these three consecutive integers is 8.