# The sum of a two-digit number and the number formed by reversing the digits 88. If the difference of the digits is 2, determine the number.

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by dweejareddy

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by dweejareddy

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Let y = the units

:

Write an equation for each statement:

:

"the sum of a two digit number and the number formed by reversing the order digits is 88."

(10x + y) + (10y + x) = 88

11x + 11y = 88

Simplify, divide by 11

x + y = 8

:

"if difference of the digits is 2 and the units digit is greater."

y - x = 2

we can use elimination with the 1st equation

y - x = 2

y + x = 8

--------------Adding eliminates x, find y

2y = 10

y = 5 is the units digit

then

5 - 2 = 3 is 10's digit

:

35 is the number

:

:

:

Check solution in the 1st statement:

the sum of a two digit number and the number formed by reversing the order digits is 88.

35 + 83 = 88

then xy +yx = 88

x- y = 2

Take the set 2 of numbers whose difference is 2

They can be 1,3 or 2,4 or 3,5 or 4,6.......................

verify the condition for the possible sets

let us start with 4,6

46 + 64 =110 which exceeds 88

so next verification would be for 3,5

35 + 53 = 88

SO the set is 3,5 and the number nay be either 35 or 53