SOLUTION: Brian O'Reilly earns twice as much each week as a tutor than he does pumping gas. His total weekly wages are $150 more than that of his younger sister. She earns one quarter as muc

Algebra ->  Graphs -> SOLUTION: Brian O'Reilly earns twice as much each week as a tutor than he does pumping gas. His total weekly wages are $150 more than that of his younger sister. She earns one quarter as muc      Log On


   

Question 227432: Brian O'Reilly earns twice as much each week as a tutor than he does pumping gas. His total weekly wages are $150 more than that of his younger sister. She earns one quarter as much as Brian does as a tutor. How much does Brian earn as a tutor?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t= Brian's weekly earnings as a tutor
Let g= Brian's weekly earnings pumping gas
LKet s= Sister's weekly earnings
given:
(1) t+=+2g
(2) t+%2B+g+=+s+%2B+150
(3) s+=+%281%2F4%29%2At
This is 3 equations and 3 unknowns, so it's solvable
First, substitute (3) in (2)
(2) t+%2B+g+=+s+%2B+150
(2) t+%2B+g+=+%281%2F4%29%2At+%2B+150
Now solve (1) for g and substitute in (2)
(1) t+=+2g
g+=+t%2F2
(2) t+%2B+g+=+%281%2F4%29%2At+%2B+150
t+%2B+t%2F2+=+t%2F4+%2B+150
t+%2B+t%2F4+=+150
1.25t+=+150
t+=+120
and, from (1)
g+=+t%2F2
g+=+60
and, from (3)
s+=+t%2F4
s+=+30
Brian earns $120/wk as a tutor
check:
(2) t+%2B+g+=+s+%2B+150
(2) 120+%2B+60+=+30+%2B+150
180+=+180
OK