Select the correct answerThe 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?Options3235cannot be determined.2734
Question
Select the correct answerThe 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?Options3235cannot be determined.2734
Solution
Let's denote the tens digit as X and the units digit as Y.
Given that the sum of the two digits is 12, we can write this as: X + Y = 12 ---- (1)
The difference between the two-digit number and the number obtained by interchanging the digits is 18. This can be written as: 10X + Y - (10Y + X) = 18 This simplifies to: 9X - 9Y = 18 Dividing through by 9 gives: X - Y = 2 ---- (2)
We can solve these two equations simultaneously. Adding equation (1) and equation (2) gives: 2X = 14 So, X = 7.
Substituting X = 7 into equation (1) gives: 7 + Y = 12 So, Y = 5.
The product of the two digits is therefore 7 * 5 = 35.
So, the correct answer is 35.
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