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

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 $x + y + z = 440$

Barbara gets 2 times as much as allie.

This means that $y = 2x$

Carson gets 1/3 as much as barbara.

This means that $z = \frac{y}{3} = \frac{2x}{3}$

Finding x:

Replacing in the first equation.

$x + y + z = 440$

$x + 2x + \frac{2x}{3} = 440$

Multiplying everything by 3

$3x + 6x + 2x = 1320$

$11x = 1320$

$x = \frac{1320}{11}$

$x = 120$

Finding y and z:

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

$z = \frac{y}{3} = \frac{240}{3} = 80$

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