SOLUTION: Hi Jason Alice frank and candy had a total of $994.00. Jason spent a quarter of his money and Alice received some more money to triple what she had at first. Frank spent 50 dollar

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Question 1206974: Hi
Jason Alice frank and candy had a total of $994.00. Jason spent a quarter of his money and Alice received some more money to triple what she had at first. Frank spent 50 dollars and candy received $90. Now they all had equal amounts of money. How much did each have at first.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Jason    j           3j/4
Alice    a           3a
Frank    f            f-50
Candi    c            c+90
TOTAL    994

system%28j%2Ba%2Bf%2Bc=994%2C3j%2F4=f-50%2C3a=f-50%2Cc%2B90=f-50%29
Can you find a way to transform this system into one equation in one unknown variable?
Use the equations 2, 3, 4, to create one single equation in one unknown variable!

Equations 2, 3, and 4 give, j, a, and c, in terms of f.
system%28j=4f%2F3-200%2F3%2Ca=f%2F3-50%2F3%2Cc=f-140%29

Substitute into the TOTAL 994 equation.
4f%2F3-200%2F3%2Bf%2F3-50%2F3%2Bf%2Bf-140=994
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steps to solve
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highlight%28f=332%29

Finding the others is straightforward.
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Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


I didn't look at the system of equations the other tutor showed in his response. IF his system of equations is correct, you might be able to find the solution solving the problem that way. Notice that in his response he did not solve the problem -- very likely because the solution by that method is not easy.

Given that the four people had equal amounts at the end, this looks like a problem that is perfectly suited for working backwards. So...

Let x = amount each had at the end.

Jason spent 1/4 of his money, so he had 3/4 of his money left. The amount he had at the start was then (4/3)x.

Alice received some money, giving her 3 times as much as she started with, so the amount she started with was (1/3)x.

Frank spent 50 dollars, so the amount he started with was x+50.

Candy received 90 dollars, so the amount she started with was x-90.

The total they had together was $994:

%284%2F3%29x%2B%281%2F3%29x%2B%28x%2B50%29%2B%28x-90%29=994
%285%2F3%29x%2Bx%2Bx=994-50%2B90
%2811%2F3%29x=1034
11x=3102
x=3102%2F11=282

ANSWERS:
Jason: (4/3)x = $376
Alice: (1/3)x = $94
Frank: x+50 = $332
Candy: x-90 = $192

CHECK: $376 + $94 + $332 + $192 = $994