Questions: Preston picked five playing cards and got a 2,3,6,5, and 1. a. What two-digit and three-digit numbers could he create that would have the greatest sum? Is there more than one possibility? What is that sum? b. What two-digit and three-digit numbers could he create that would have the smallest sum? Is there more than one possibility? What is that sum?

Preston picked five playing cards and got a 2,3,6,5, and 1. a. What two-digit and three-digit numbers could he create that would have the greatest sum? Is there more than one possibility? What is that sum? b. What two-digit and three-digit numbers could he create that would have the smallest sum? Is there more than one possibility? What is that sum?
Transcript text: 3-76. Preston picked five playing cards and got a $2,3,6,5$, and 1 . a. What two-digit and three-digit numbers could he create that would have the greatest sum? Is there more than one possibility? What is that sum? b. What two-digit and three-digit numbers could he create that would have the smallest sum? Is there more than one possibility? What is that sum?
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Solution

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Solution Steps

To solve this problem, we need to form two-digit and three-digit numbers using the given digits (2, 3, 6, 5, and 1) and calculate their sums. For part (a), we aim to maximize the sum, so we should use the largest digits for the three-digit number and the remaining largest for the two-digit number. For part (b), we aim to minimize the sum, so we should use the smallest digits for the three-digit number and the remaining smallest for the two-digit number.

Step 1: Identify the Digits

The digits available for forming numbers are \(2, 3, 6, 5, 1\).

Step 2: Maximize the Sum

To find the two-digit and three-digit numbers that yield the greatest sum, we can form the numbers \(51\) (two-digit) and \(632\) (three-digit). The sum is calculated as follows:

\[ \text{Max Sum} = 51 + 632 = 683 \]

Step 3: Minimize the Sum

To find the two-digit and three-digit numbers that yield the smallest sum, we find that no valid combination exists that uses all digits to form a two-digit and a three-digit number. Therefore, the minimum sum is undefined in this context.

Final Answer

For part (a), the maximum sum is \(683\) with the combination of \(51\) and \(632\). For part (b), there is no valid combination, hence the minimum sum is undefined.

Thus, the answers are:

  • Part (a): \( \boxed{683} \)
  • Part (b): No valid combination.
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