SOLUTION: Please help me understand the steps for solving this problem. The value of a two-digit number is twice as large as the sum of its digits. If the digits were reversed, the resultin
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Question 240364: Please help me understand the steps for solving this problem. The value of a two-digit number is twice as large as the sum of its digits. If the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find the original number. Answer by scott8148(6628) (Show Source):
"The value of a two-digit number is twice as large as the sum of its digits" ___ 10t + u = 2(t + u)
___ 10t + u = 2t + 2u
___ 8t = u ___ (there is only one pair of digits that works here)
"If the digits were reversed, the resulting number would be 9 less than 5 times the original number"
___ 10u + t = 5(10t + u) - 9
___ 10u + t = 50t + 5u - 9
___ 5u + 9 = 49t
substitute the value of u from the 1st part to find the value of t
___ then substitute t back to the 1st part to find the value of u
