If the hundreds digit and the units digit are reversed the new number will be

# If the hundreds digit and the units digit are

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sum of the tens and the hundreds digit. If the hundreds digit and the units digit are reversed, the new number will be 198 more than the original number. What is the number? Solution: We start with the representations: Let H = Hundreds digit T = Tens digit U = Units digit 100H + 10T + U = the original number 100U + 10T + H = the new number (when the hundreds and units digits are reversed) NOTE: Please avoid the common mistake of representing a three-digit number by simply putting the representations for the digits beside each other (e.g., HTU). Remember that in Algebra, placing variables beside each other means multiplication.
Word Problems Our equations are: H + T + U = 8 (“the sum of the digits is 8”) 2U = (T + H) +1 (“Twice the units digit is one more than the sum of the tens and the hundreds digit”) 100U + 10T + H = (100H + 10T + U) + 198 (“If the hundreds digit and the units digit are reversed, the new number will be 198 more than the original number) After simplifying our equations, our system would be H + T + U = 8 H T + 2U = 1 H + U = 2 The number is 143.

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• Fall '13
• Staff
• Numerical digit, Sophy

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