Answer:
Allie got $120, Barbara got $240 and Carson got $80.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
Allie got x.
Barbara got y.
Carson got z.
Divide $440 among themselves
This means that [tex]x + y + z = 440[/tex]
Barbara gets 2 times as much as allie.
This means that [tex]y = 2x[/tex]
Carson gets 1/3 as much as barbara.
This means that [tex]z = \frac{y}{3} = \frac{2x}{3}[/tex]
Finding x:
Replacing in the first equation.
[tex]x + y + z = 440[/tex]
[tex]x + 2x + \frac{2x}{3} = 440[/tex]
Multiplying everything by 3
[tex]3x + 6x + 2x = 1320[/tex]
[tex]11x = 1320[/tex]
[tex]x = \frac{1320}{11}[/tex]
[tex]x = 120[/tex]
Finding y and z:
[tex]y = 2x = 2(120) = 240[/tex]
[tex]z = \frac{y}{3} = \frac{240}{3} = 80[/tex]
Allie got $120, Barbara got $240 and Carson got $80.
