Michelle and her brothers sam and dean are saving money over summer break each week michelle saves three times as much as sam sam saves $2 more than dean at the end of 5 weeks the three of them have saved a total of 240 how much money did each person spend

I believe you want to know how much each of them SAVED.

Let the amount saved by Michelle be x, the amount saved by Sam be y and the amount saved by Dean be z.

From the givens:
x = 3y (Michelle saves 3 times as much as Sam)eq1
y = 2+z (Sam saves 2$ more than Dean)
z=y-2eq 2
x+y+z = 240 (total amount)eq 3

substitute by equation 1 in 3:
3y+y+z=240
4y+z=240eq 4

substitute by 2 in 4:
4y+y-2=240
5y=242
y= 48.4$

from 1:
x=3y
x=145.2$

from 2:
z=y-2
z=46.4$