Given that a,b,c,d,ea,b,c,d,e are distinct whole numbers from 11 to 99 inclusive, along with the equality ab=c⋅100+d⋅10+eab=c⋅100+d⋅10+e where c⋅100+d⋅10+ec⋅100+d⋅10+e is the largest possible value, find the value of a+b+c+d+e.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Given that a,b,c,d,ea,b,c,d,e are distinct whole numbers from 11 to 99 inclusive, along with the equality

ab=c⋅100+d⋅10+eab=c⋅100+d⋅10+e

where c⋅100+d⋅10+ec⋅100+d⋅10+e is the largest possible value, find the value of

a+b+c+d+e.
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