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Tine and Kassy spent $225 on a shopping spree.  All items they purchased were whole-dollar amounts.  All the prices were prime numbers, and each digit (1 through 9)was used exactly once among all the prices.  For three of the items, the sum of the digits in the price was 5.  What was the value of each item? Please explain.

User Garren S
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Tine and Kassy spent $225 on a shopping spree, buying items with prime numbers whose digits sum to 5. The unique combination fulfilling these conditions is $23, $32, and $14, with each digit from 1 to 9 used exactly once among the prices.

To solve this problem, let's consider the prime numbers whose digits sum to 5 and whose digits include each number from 1 to 9 exactly once.

The prime numbers whose digits sum to 5 and contain distinct digits are limited. We can find three such numbers: 23, 32, and 14. The sum of digits in each of these numbers is 5.

Now, we can consider the different combinations of these prime numbers to form unique three-item sets whose sum is $225.

23 + 32 + 14 = $69

23 + 14 + 32 = $69

32 + 23 + 14 = $69

32 + 14 + 23 = $69

14 + 23 + 32 = $69

14 + 32 + 23 = $69

The unique combination is 23 + 32 + 14 = $69, where each digit from 1 to 9 is used exactly once.

Therefore, the values of the three items are $23, $32, and $14.

User Matias Kinnunen
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