Lesson Sum of Digits Problems

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 This Lesson (Sum of Digits Problems) was created by by oberobic(2304)  : View Source, ShowAbout oberobic: MBA/Ph.D. University Administrator Problem: We are told that a certain two-digit number has a value that is three times the sum of its digits. Also, the units digit is one more than tree times the tens digit. Find the number. . Solution: Solving "sum of digits" problems hinges on remembering that any "number" is simply a visual representation of the number of ones, the number of tens, the number of hundreds, etc. A two-digit number, for example 23, really means 10*2 + 1*3 = 23. . To solve this problem, let x = tens, and y = ones. We would write the number as xy = 23, Each x is valued at 10x, and y is valued at 1. So the representation 23 would mean 10*2 + 3*1. . Note well that, for this problem, when we show 'xy', we only mean 'x' sitting next to 'y', not x times y. . We also are told the two-digit number, xy, that has a value '3 times the sum of its digits'. That means the value of the expression is 3 * sum of digits. . The sum of digits is simply x + y. So, 3 times the sum of digits is just 3*(x+y) or 3(x+y). . Since we know each x is worth 10 and each y is worth 1, then we can say the numeric value is: 10x + y = 3 * (x + y) . At this point we have only one equation, but it has two unknowns. That is unsolvable. . But looking back at the problem we see another relationship is given. The units digit (y) is one more (+1) than 3 times the tens digit (3x). So, y = 3x+1 . Now we can substitute that fact into our equation. . 10x + 3x+1 = 3 * (x + 3x+1) 10x + 3x +1 = 3x + 9x + 3 13x + 1 = 12x + 3 x = 2 . We know from the setup that: y = 3x + 1 y = 3*2 + 1 y = 7 . Now we have a solution: the 2-digit number is xy = 27. . Again, remember this is not x times y, but just x beside y. . Always check your work to determine the proposed solution is the correct answer. . What is the sum of digits? 2+7 = 9 What is 3 times the sum of digits? 3*(2+7) = 27 Is that the same as xy? Yes. So the solution is the answer we were seeking. . Answer: The number is 27. This lesson has been accessed 3350 times.