he sum of five distinct whole numbers is 337. If 60 is the smallest of them, what is the maximum value the largest number can have?Options :917097274

1. Break Down the Problem

To find the maximum value of the largest number among five distinct whole numbers that sum up to 337, where the smallest number is given as 60.

Let the five distinct whole numbers be $a_1, a_2, a_3, a_4, a_5$ such that:

• $a_1 = 60$ (the smallest number)
• $a_5$ is the largest number we want to maximize.

Given that the numbers must be distinct and whole, the conditions are:

• $a_1 < a_2 < a_3 < a_4 < a_5$
• $a_1 + a_2 + a_3 + a_4 + a_5 = 337$

2. Relevant Concepts

We need to express the problem in terms of the numbers: $60 + a_2 + a_3 + a_4 + a_5 = 337$ This simplifies to: $a_2 + a_3 + a_4 + a_5 = 337 - 60 = 277$ To maximize $a_5$, we need to minimize $a_2$, $a_3$, and $a_4$ under the constraint of distinct whole numbers.

3. Analysis and Detail

To minimize $a_2, a_3, a_4$:

1. The smallest whole number greater than 60, which is $61$ (for $a_2$).
2. The next smallest would be $62$ for $a_3$.
3. Then $63$ for $a_4$.

Now we substitute these values: $a_2 = 61, \quad a_3 = 62, \quad a_4 = 63$

Calculating their sum: $a_2 + a_3 + a_4 = 61 + 62 + 63 = 186$

Therefore: $a_5 = 277 - 186 = 91$

4. Verify and Summarize

The five distinct whole numbers would be: $60, 61, 62, 63, 91$. We verified the sum: $60 + 61 + 62 + 63 + 91 = 337$ The conditions of being distinct and whole numbers are met.

Final Answer

The maximum value the largest number can have is $91$.