Question 1096872: Ms. Nguyen is in debt to her mother, her brother, and her sister, for a total of $410. She owes her brother $10 less than five times what she owes her mother. She owes her sister $35 more than she does her mother. How much money does she owe to each? Define a variable, then write and solve an equation. To check your answer, make sure that the sum of her three debts is still $410.
Found 2 solutions by jorel1380, ikleyn:
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! Let m be what Ms. Nguyen owes her mother. Then her brother is owed 5m-10; and her sister m+35. So
m+5m-10+m+35=410
7m=385
m=55
5m-10=265
m+35=90
☺☺☺☺
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
Let M be the amount Ms. Nguen is in debt to her mother (in dollars).
Then the amount Ms. Nguen is in debt to her brother is 5M-10 dollars.
Also, the amount Ms. Nguen is in debt to her sister is (M + 35) dollars.
In all,
M + (5M-10) + (M+35) = 410. (1)
So, M is your variable and (1) is your equation.
To solve it, simplify
7M + 25 = 410 ====> 7M = 410-25 = 395 ====> M =  = 55 dollars.
Answer. The debt to the mother is $55. The debt to the brother is 5*55-10 = $265. The debt to the sister is 55+35 = $90.
Check. 55 + 265 + 90 = 410 dollars. ! Correct !
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