SOLUTION: A number with two digits exceeds twice the sum of its digits by 26. If the digits are interchanged, the resulting number exceeds the given number by 18. Find the number.

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Question 1193002: A number with two digits exceeds twice the sum of its digits by 26.
If the digits are interchanged, the resulting number exceeds the
given number by 18. Find the number.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
system%28u%2B10t=2%28u%2Bt%29%2B26%2Cand%2C10u%2Bt=u%2B10t%2B18%29

u%2B10t=2u%2B2t%2B26and9u-9t=18

-u%2B8t=26%2Cu-t=2

Add:
7t=28
highlight%28t=4%29

Using simplified equation 1,
-u%2B8t=26
u-8t=-26
u=8t-26
u=8%2A4-26
u=32-26
highlight%28u=6%29

The number is 46.