Product and Sum of Digits = NumberDate: 10/24/2001 at 18:58:17 From: Meghan Jordan Subject: Word problem... How many two-digit numbers exist such that when the products of their digits are added to the sums of their digits, the result is equal to the original two-digit number? Date: 10/25/2001 at 11:05:19 From: Doctor Ian Subject: Re: Word problem... Hi Meghan, A two digit number looks like ab which is just shorthand for 10a + b where a is between 1 and 9, and b is between 0 and 9. The product of the digits would be a*b The sum of the digits would be a+b So if the number is equal to the product of the digits plus the sum of the digits, then 10a + b = (a*b) + (a+b) = a*b + a + b = (b+1)*a + b Now, this is interesting, because it means that b+1 must be equal to 10. So that certainly narrows things down a bit. Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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