the sum of one fifth of an integer and one tenth of that integer is at most 20. find the greatest possible integer.
x/5 + x/10 <= 20
x <= 200/3
so, x <= 66
if x is an integer, write three consecutive integers beginning with the integer x-2.
x -2 _____ ______
To find the greatest possible integer, let's break down the given information step by step.
Let's assume the integer is represented by "x".
According to the problem, "the sum of one-fifth of an integer and one-tenth of that integer is at most 20." Mathematically, this can be written as:
1/5x + 1/10x ≤ 20
To simplify the equation, let's find a common denominator:
2/10x + 1/10x ≤ 20
Combining like terms, we have:
3/10x ≤ 20
To solve for x, we need to isolate it. Multiply both sides of the inequality by 10/3:
(10/3) * (3/10x) ≤ (10/3) * (20)
Simplifying, we get:
x ≤ 200/3
To find the greatest possible integer, we need to round down this decimal value since we're looking for a whole number. So, the greatest possible integer will be the integer part of 200/3, which is 66.
Therefore, the greatest possible integer is 66.