Let person 1 = x, person 2 = y, and person 3 = z. So three people have to share $80. If this is the case, we can assume this equation:
x + y + z = 80 (because the amount of money that each of the three have will add up to $80.)
The second person, y, has to have twice as much as the first person, x. Meaning we can assume the equation: Y = 2x. Therefore:
x + (2x) + z = 80
3x + z = 80
The third person, z, has to have $5 less than the second person, y. Meaning we can assume the equation z = y - 5 (however, we want to keep the x + y + z = 80 equation in terms of only one variable, x. So, in z = y - 5, we can replace the y with 2x, making it z = 2x - 5).
3x + (2x - 5) = 80
5x - 5 = 80
5x = 75
x = 15
The first person will have $15. We can determine what the other two people will get using only this bit of information, and our previously assumed equations. If we recall, our other two equations were:
y = 2x and z = 2x - 5
They both have the x variable in them. Simply plug in the value for x into these two equations.
y = 2(15)
y = 30
z = 2(15) - 5
z = 25
The question asks how much the third person will get. And we made the third person = z. So the third person will get $25.
