SOLUTION: Brian earns twice as much as a tutor as he does pumping gas. His total weekly wages are $150 more than his sister. She earns one quarter as much as Brian does as a tutor. How much

Algebra ->  Expressions-with-variables -> SOLUTION: Brian earns twice as much as a tutor as he does pumping gas. His total weekly wages are $150 more than his sister. She earns one quarter as much as Brian does as a tutor. How much       Log On


   

Question 818154: Brian earns twice as much as a tutor as he does pumping gas. His total weekly wages are $150 more than his sister. She earns one quarter as much as Brian does as a tutor. How much does Brian earn as a tutor?
Thank you.
Answer by LinnW(1048) About Me  (Show Source):
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Brian earns twice as much as a tutor as he does pumping gas. His total weekly wages are $150 more than his sister. She earns one quarter as much as Brian does as a tutor. How much does Brian earn as a tutor?
B = Brians earnings as tutor
S = Sisters earnings
Since Brian earns twice as much as a tutor as pumping gas,
we can represent the amount he makes pumping gas as (1/2)B.
B + (1/2)B = S + 150
(3/2)B = S + 150
S = (1/4)B
If we substitute (1/4)B for S in the first equation we have
(3/2)B = (1/4)B + 150
Subtract (1/4)B from each side.
(3/2 - 1/4)B = 150
(6/4 - 1/4)B = 150
(5/4)B = 150
Multiply each side by 4/5
B = (4/5)150
B = 600/5
B = 120