The number obtained by interchanging the two digits of a two-digit number is less than the original number by 18. The sum of the two digits of the number is 16. What is the original number?*2 pointsYour answer
Question
The number obtained by interchanging the two digits of a two-digit number is less than the original number by 18. The sum of the two digits of the number is 16. What is the original number?*2 pointsYour answer
Solution
Let's denote the tens digit as X and the units digit as Y.
From the problem, we know that:
-
X + Y = 16 (The sum of the two digits is 16)
-
10X + Y - (10Y + X) = 18 (The number obtained by interchanging the two digits of a two-digit number is less than the original number by 18)
Solving these two equations, we get:
- X = 16 - Y
Substitute X in the second equation:
- 10(16 - Y) + Y - (10Y + 16 - Y) = 18 160 - 10Y + Y - 10Y + Y - 16 = 18 -18Y = -126 Y = 7
Substitute Y = 7 in the first equation:
X = 16 - 7 = 9
So, the original number is 97.
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