What is the linear equation that will represent the second statement in the following problem:

"The sum of the digits of a three-digit number is 12. If the hundreds digit is replaced by the tens digit, the tens digit by the units digit, and the units digit by the hundreds digit, the new number is greater than the original number by 108. If the tens and the hundreds digits are interchanged, the original number is 90 less than the number formed. Find the original number."

100t+10u+h = 100h+10t+u + 108

Four digit number. Greater than 4000. Sum of its hundreds digit and it's ones digit is 9. Twice it's tens digit is 2 more than its thousands digit. Sum of one- fifth of its hundreds digit and two-thirds of its ones digit is 6. It's 10 digit is 1 less than its thousands digit.

a + b + c = 12

100b + 10c + a - ( 100a + 10b + c ) = 108

100b + 10a + c - ( 100a + 10b + a ) = 90

To find the linear equation that represents the second statement in the problem, we need to translate the given information into mathematical equations.

Let's first define the original three-digit number as XYZ, where X represents the hundreds digit, Y represents the tens digit, and Z represents the units digit.

From the statement, "If the hundreds digit is replaced by the tens digit, the tens digit by the units digit, and the units digit by the hundreds digit, the new number is greater than the original number by 108," we can create the equation:

100Z + 10X + Y = 100X + 10Y + Z + 108

This equation represents the value of the new number (100Z + 10X + Y) being greater than the original number (100X + 10Y + Z) by 108.

Next, from the statement "If the tens and the hundreds digits are interchanged, the original number is 90 less than the number formed," we can form another equation:

100X + 10Y + Z = 100Y + 10X + Z + 90

This equation represents the value of the original number (100X + 10Y + Z) being 90 less than the number formed by interchanging the tens and hundreds digits (100Y + 10X + Z).

These two equations form a system of linear equations that can be solved to find the values of X, Y, and Z, which represent the hundreds, tens, and units digits of the original number.

To solve this system of equations, we can use algebraic methods such as substitution or elimination. Once we have the values of X, Y, and Z, we can combine them to find the original number XYZ.