The sum of three consecutive natural numbers, each divisible by 5, is 225. What is the largest of these three numbers?

Introduction / Context:
This question combines consecutive numbers with divisibility by a fixed integer. The three natural numbers are consecutive multiples of 5 and their sum is given. You must find the largest of them. Problems like this build comfort with arithmetic progressions and basic divisibility rules in a natural numbers context.

Given Data / Assumptions:
- There are three consecutive natural numbers, each divisible by 5.
- Being consecutive and divisible by 5 means they are consecutive multiples of 5, such as 5k, 5(k + 1), and 5(k + 2).
- Their sum is 225.
- We need to find the largest of these three numbers.

Concept / Approach:
Multiples of 5 can be written as 5 times an integer. If we denote the smallest multiple by 5k, the next two consecutive multiples are 5(k + 1) and 5(k + 2). Their sum can be simplified to a single expression in k, leading to a linear equation. Solving this equation determines k, and from there we can find each of the three numbers and identify the largest.

Step-by-Step Solution:
Step 1: Let the three consecutive multiples of 5 be 5k, 5(k + 1), and 5(k + 2).Step 2: Write their sum: 5k + 5(k + 1) + 5(k + 2).Step 3: Factor out 5: 5[k + (k + 1) + (k + 2)] = 5[3k + 3].Step 4: The sum is given as 225, so 5[3k + 3] = 225.Step 5: Divide both sides by 5 to get 3k + 3 = 45.Step 6: Subtract 3 from both sides: 3k = 42.Step 7: Divide both sides by 3 to solve for k: k = 14.Step 8: The three numbers are 5k = 5 * 14 = 70, 5(k + 1) = 5 * 15 = 75, and 5(k + 2) = 5 * 16 = 80.Step 9: Among these, the largest number is 80.

Verification / Alternative check:
Check the sum of the numbers 70, 75, and 80. Their sum is 70 + 75 + 80 = 225, which matches the given total. Also, all three numbers are divisible by 5, and they are consecutive multiples of 5 because the differences between them are 5. This confirms that our algebraic approach is correct and that 80 is indeed the largest of the three numbers.

Why Other Options Are Wrong:
If the largest number were 85, then the three consecutive multiples of 5 would be 75, 80, and 85, whose sum is 240, not 225. If the largest number were 75, the three numbers would be 65, 70, and 75, whose sum is 210. Similarly, a largest number of 70 or 90 would produce sums that do not equal 225. Therefore, those options do not satisfy the condition given in the question.

Common Pitfalls:
A typical mistake is to assume that the three numbers are 5 apart overall instead of 5 apart between consecutive terms. Another common error is setting them as 5k - 5, 5k, and 5k + 5 but then miscomputing the sum. Using the expression 5k, 5(k + 1), and 5(k + 2) and simplifying systematically avoids confusion and keeps the algebra very clear.

Final Answer:
The largest of the three numbers is 80.