Three students open e-trade accounts and become day traders. Although they all work hard, they achieve the following steady rates of losing money: The first student loses $1000 in one hour, the second student loses $1000 in two hours, and the third student loses $1000 in three hours. Find the number of minutes it takes for the three students together to lose a total of $2000.


Last week’s solution

45. From the definition, the first and second digits of an upright integer automatically determine the third digit, which is the sum of the first two digits. Consider those upright integers beginning with 1: 101, 112, 123, 134, 145, 156, 167, 178, and 189; there is a total of 9 such numbers. (Note that the second digit may not be 9; otherwise, the last digit would be 1+9=10.) Beginning with 2, the upright integers are 202, 213, 224, 235, 246, 257, 268, and 279; there is a total of 8 such numbers. We may continue this pattern of analysis to show that the numbers of upright integers beginning with a digit of 3, 4, 5, 6, 7, 8, or 9 are 7, 6, 5, 4, 3, 2, and 1, respectively.

Therefore, there is a total of 9+8+7+6+5+4+3+2+1=45 three-digit upright integers.


From Eric Lass, 7th & 8th grade Math Teacher


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