Question

Allie, barbara, and carson will divide $440 among themselves as follows. Barbara gets 2 times as much as allie. Carson gets 1/3 as much as barbara. How much does each person get?

Answer 1

Allie got $120, Barbara got $240 and Carson got $80.

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
`x + y + z = 440`

Barbara gets 2 times as much as allie.

This means that
`y = 2x`

Carson gets 1/3 as much as barbara.

This means that
`z = (y)/(3) = (2x)/(3)`

Finding x:

Replacing in the first equation.

`x + y + z = 440`

`x + 2x + (2x)/(3) = 440`

Multiplying everything by 3

`3x + 6x + 2x = 1320`

`11x = 1320`

`x = (1320)/(11)`

`x = 120`

Finding y and z:

`y = 2x = 2(120) = 240`

`z = (y)/(3) = (240)/(3) = 80`

Allie got $120, Barbara got $240 and Carson got $80.