# The sum of the digits of a two digit number is 11.the number obtained by interchanging the digits exceeds the given number by 45.find the number

1
by jeniselva13

how we get -9u-9t=-99?

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by jeniselva13

how we get -9u-9t=-99?

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u = 1's digit

t + u = 11

10u + t = 45 + (10t + u)

Combine like terms: 9u - 9t = 45

Solve by elimination:

9u - 9t = 45

Now, we know that u +t = 11

multiply -9 on both sides...

-9(u+t)=-99

-9u -9t = -99

-18t = -54

t = 3, u = 8

Original number is 38.