Respuesta :
21 percentage of four-digit integers above 5000 have a thousands digit that is equal to the sum of the other three digits.
Given that,
We have to find what percentage of four-digit integers above 5000 have a thousands digit that is equal to the sum of the other three digits.
We know that,
The other three numerals must add up to 5 because the first digit is 5.
The other two digits must add up to 5 if the second digit is 0, thus they
are 0+5, 1+4, or 2+3 or their reverses 5+0, 4+1, and 3+2, that 6
The last two numbers must add up to 4 if the second digit is 1, thus they
are 0+4, 1+3, or 2+2. There are five more since the first two are reversed.
The last two digits must add up to 3 if the second digit is 2, thus they
are 0+3 and 1+2, and their reverses, so that's 4 more.
If the second digit is 3, the last two digits must sum to 2, so they
are 0+2 and 1+1 and the reverse of the first, so that's 3 more.
The last two digits must add up to 1, so if the second digit is 4, they must.
are 0+1 and its reverse, so that's 2 more
If the second digit is 5, the last two digits must sum to 0, so they
are 0+0, so that's 1 more.
Total = 6+5+4+3+2+1 = 21.
Therefore, 21 percentage of four-digit integers above 5000 have a thousands digit that is equal to the sum of the other three digits.
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