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Explanation:
For the original two digit number, we have:
The original number is 10x+y. For instance, if x = 5 and y = 7, then we have 10x+y = 10*5+7 = 57.
This original number 10x+y swaps its digits to 10y+x. Then we add up the two expressions:
(original)+(swapped) = (10x+y)+(10y+x) = 11x+11y = 11(x+y)
This sum is stated to be 154
11(x+y) = 154
x+y = 154/11
x+y = 14
Then we're told that "the ones digit in it (the original number) is 2 less than the tens digit". Meaning that y = x-2 is another equation we can use. We'll plug this into the previous equation we found and solve for x
x+y = 14
x+x-2 = 14 ... replace y with x-2
2x-2 = 14
2x = 14+2
2x = 16
x = 16/2
x = 8 is the tens digit of the original number
y = x-2
y = 8-2
y = 6 is the units digit of the original number
The original number is 10x+y = 10*8+6 = 86
As a check, adding 86+68 = 154 which confirms our answer.
