SOLUTION: A total of $55 is divided among Ben, John, and Mary. John got 1/3 of what Ben got, while Mary got 1/2 of what Ben got. How much did each recieve? I am not sure how to convert

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Question 583042: A total of $55 is divided among Ben, John, and Mary. John got 1/3 of what Ben got, while Mary got 1/2 of what Ben got. How much did each recieve?

I am not sure how to convert this to algebra form. I should be able to solve once I get the correct form, but I would appreciate the help to be sure I am getting the correct steps.
Thank you

Found 2 solutions by JBarnum, solver91311:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
j=john b=ben m=mary
j=%281%2F3%29b
m=%281%2F2%29b
j%2Bm%2Bb=55
substitute the j and m and solve for ben
%281%2F3%29b%2B%281%2F2%29b%2Bb=55 find a common denom number to knock out the fractions (6) is divisable by 3, 2, and 1 so cross canceling will eliminate the fractions
b%2F3%2Bb%2F2%2Bb=55 multiply everything by 6
2b%2B3b%2B6b=330
11b=330
b=30
substitute in b for the other two equations
j=10
m=15
.
check
j+m+b=55
10+15+30=55
55=55
correct

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent what Ben got. Then is what John got, and is what Mary got. And then:



Solve for , then calculate and .

John

My calculator said it, I believe it, that settles it
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