SOLUTION: A sum of money is shared between Jasmine and Luisa in the ratio of 4:5. If Luisa were to give $9 to Jasmine, they would have the same amount of money. How much money does Luisa h

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A sum of money is shared between Jasmine and Luisa in the ratio of 4:5. If Luisa were to give $9 to Jasmine, they would have the same amount of money. How much money does Luisa h      Log On


   

Question 832295: A sum of money is shared between Jasmine and Luisa in the ratio of 4:5. If Luisa were to give $9 to Jasmine, they would have the same amount of money. How much money does Luisa have?
I worked the problem in what I think is the correct way, and I got the following:
Luisa has $36. If she gave $9 to Jasmine, they would each have $27. So Jasmine currently has $18. Together they share $54.

Here is how I set up the problem:

X/X+9 = 4/5

I cross multiplied to get 5x = 4 (x + 9); 5x = 4x + 36; solve for x to get x = 36.
Please let me know if this is correct. If it is incorrect, please let me know how I should have done it.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Original sum of money, x for Jasmine and y for Luisa, the sum being x%2By, which we do not yet know the values.. x%2Fy=4%2F5

Luisa gives $9 to Jasmine. Their monies are then x+9 and y-9. These quantities are then given in the description as EQUAL. This means x%2B9=y-9.

This situation has the symbolic description of :
x%2Fy=4%2F5 and x%2B9=y-9.
We may use the nine-dollar shift equation to solve for y, and substitute into the ratio equation, as you seem to have done.
y=x%2B9%2B9
y=x%2B18
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Ratio x%2Fy=4%2F5
highlight%28x%2F%28x%2B18%29=4%2F5%29, somewhat different from what you obtained.

Solve that one, highlight%28x%2F%28x%2B18%29=4%2F5%29, and you should find the correct values for x and y. The original amounts for the parts of the sum of money which Jasmine and Luisa had.