A digital scoreboard at a school track event displays a 5-digit number. The number has these properties: - The digit in the ten-thousands place is 3. - The digit in the thousands place is 4 MORE than the digit in the hundreds place. - The digit in the tens place is 0. - The digit in the ones place is 7. - The sum of ALL five digits equals 20. What is the number on the scoreboard?
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Worked Solution
Step 1: Fix the known digits from the clues.
Ten-thousands = 3, Tens = 0, Ones = 7.
The number has the form: 3 _ _ 0 7
Step 2: Let the hundreds digit = h.
Then the thousands digit = h + 4.
The number is: 3, (h+4), h, 0, 7
Step 3: Use the digit-sum condition.
3 + (h + 4) + h + 0 + 7 = 20
2h + 14 = 20
2h = 6
h = 3
Step 4: Find the thousands digit.
Thousands = h + 4 = 3 + 4 = 7
Step 5: Write the full number.
Ten-thousands=3, Thousands=7, Hundreds=3, Tens=0, Ones=7
-> 37 307
Verification: 3+7+3+0+7 = 20 and 7-3 = 4
Correct answer: 37 307
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