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Let the ten’s and the unit’s digits in the first number be x and y, respectively. So, the first number can be written as 10x + y in the expanded form.
When the digits are reversed, x becomes the unit’s digit and y becomes the ten’s digit. This number, in the expanded notationis 10y + x.
According to the given condition.
(10x + y) + (10y + x) = 66
11(x + y) = 66
x + y = 6 .....(1)
You are also given that the digits differ by 2.
Therefore,
either x – y = 2 ... (2)
or y – x = 2 ... (3)
If x – y = 2, then solving (1) and (2) by elimination, you get x = 4 and y = 2. In this case, the number is 42.
If y – x = 2, then solving (1) and (3) by elimination, you get x = 2 and y = 4. In this case, the number is 24.
Thus, there are two such numbers 42 and 24.
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When the digits are reversed, x becomes the unit’s digit and y becomes the ten’s digit. This number, in the expanded notationis 10y + x.
According to the given condition.
(10x + y) + (10y + x) = 66
11(x + y) = 66
x + y = 6 .....(1)
You are also given that the digits differ by 2.
Therefore,
either x – y = 2 ... (2)
or y – x = 2 ... (3)
If x – y = 2, then solving (1) and (2) by elimination, you get x = 4 and y = 2. In this case, the number is 42.
If y – x = 2, then solving (1) and (3) by elimination, you get x = 2 and y = 4. In this case, the number is 24.
Thus, there are two such numbers 42 and 24.
----------×----------×---------×-------×--------×----------×--
Hope it is helpful to you..............
If you like my answer mark me as BRAINLIST and follow me .
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