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A two-digit number is less than 6 times the sum of its digits by 1. The difference between the digit is 1. Find the number.​

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Answer:

the two-digit number is 65.

Explanation:

Let's assume that the tens and units digits of the two-digit number are x and y, respectively.

According to the given condition,

10x + y < 6(x + y) - 1 (less than 6 times the sum of its digits by 1)

Simplifying the above equation, we get:

4x - 5y < -1 (dividing both sides by 2)

Also, it is given that the difference between the digits is 1, so we can write:

x - y = 1 (difference between the digits is 1)

Now, we need to solve these two equations to find the values of x and y.

Multiplying the second equation by 4, we get:

4x - 4y = 4

Adding this equation to the first equation, we get:

4x - 5y + 4x - 4y = 3

Simplifying the above equation, we get:

8x - 9y = 3

Now, we can solve these two equations simultaneously to find the values of x and y.

Multiplying the second equation by 8, we get:

8x - 8y = 8

Subtracting this equation from the previous equation, we get:

y = 5

Substituting this value of y in the equation x - y = 1, we get:

x - 5 = 1

x = 6

Therefore, the two-digit number is 65.

User Kkakroo
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