The difference between a two-digit number and the number obtained by interchanging the two digits of the numbers is 18. The sum of the two digits of the numbers is 12. what is the product of the two digits of the two-digit number?Options34352732cannot be determined.
Question
The difference between a two-digit number and the number obtained by interchanging the two digits of the numbers is 18. The sum of the two digits of the numbers is 12. what is the product of the two digits of the two-digit number?Options34352732cannot be determined.
Solution
Let's denote the tens digit as X and the units digit as Y.
From the problem, we know that:
- X + Y = 12 (The sum of the two digits is 12)
- 10X + Y - (10Y + X) = 18 (The difference between the original two-digit number and the number obtained by interchanging the digits is 18)
Solving these two equations, we get:
- X + Y = 12
- 9X - 9Y = 18
Dividing the second equation by 9, we get X - Y = 2.
Now we have a system of two equations:
- X + Y = 12
- X - Y = 2
Adding these two equations together, we get 2X = 14, so X = 7.
Substituting X = 7 into the first equation, we get 7 + Y = 12, so Y = 5.
Therefore, the product of the two digits is 7 * 5 = 35. So, the answer is 35.
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