Sure! Let's solve the given problem step-by-step:
We need to determine an equation to solve for three numbers that meet the following conditions:
1. The sum of the three numbers is 131.
2. The second number is seven more than twice the first number.
3. The third number is 12 less than the first number.
Let's define the variables:
Let [tex]\( x \)[/tex] be the first number.
Given:
- The second number, [tex]\( y \)[/tex], is [tex]\( 2x + 7 \)[/tex] (seven more than twice the first number).
- The third number, [tex]\( z \)[/tex], is [tex]\( x - 12 \)[/tex] (12 less than the first number).
To form the equation based on the sum of these three numbers:
[tex]\[ x + y + z = 131 \][/tex]
Substitute the expressions for [tex]\( y \)[/tex] and [tex]\( z \)[/tex] into the equation:
[tex]\[ x + (2x + 7) + (x - 12) = 131 \][/tex]
Now, combine like terms:
[tex]\[ x + 2x + 7 + x - 12 = 131 \][/tex]
Simplify the equation:
[tex]\[ 4x - 5 = 131 \][/tex]
Add 5 to both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[ 4x = 136 \][/tex]
Finally, divide by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 34 \][/tex]
So, the proper and complete equation used to solve the problem is:
[tex]\[ x + (2x + 7) + (x - 12) = 131 \][/tex]
