two-thirds of a number, decreased by thirty-six, is at most twenty-two. Find the number.
(2/3)n - 36 </= 22
2 n - 108 </= 66
2 n </= 174
n </= 87
To find the number, let's break down the problem into steps:
Step 1: Translate the given information into an equation.
- Let's say the number is represented by "x".
- According to the problem, "two-thirds of a number, decreased by thirty-six, is at most twenty-two."
- Mathematically, this can be written as: (2/3)x - 36 ≤ 22.
Step 2: Solve the equation.
- We want to find the number "x" that satisfies the given inequality.
- To do this, we'll solve for "x" by isolating it on one side of the equation.
- Add 36 to both sides of the equation to get: (2/3)x ≤ 22 + 36.
- Simplify the right side of the inequality: (2/3)x ≤ 58.
- Multiply both sides of the inequality by 3/2 to get: x ≤ 58 * 3/2.
- Simplify the right side of the inequality: x ≤ 87.
Step 3: Interpret the solution.
- The solution to the equation is x ≤ 87.
- This means that any number less than or equal to 87 would satisfy the given conditions.
- However, since we're looking for a whole number, the largest possible value would be 87.
Therefore, the number you're looking for is 87.