SOLUTION: Bertram and Ernie had $988 altogether. After Bertram spent 4/5 of his money and Ernie spent 1/3 of his money they had an equal amount of money left. How much money did Ernie hove a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Bertram and Ernie had $988 altogether. After Bertram spent 4/5 of his money and Ernie spent 1/3 of his money they had an equal amount of money left. How much money did Ernie hove a      Log On


   

Question 1203822: Bertram and Ernie had $988 altogether. After Bertram spent 4/5 of his money and Ernie spent 1/3 of his money they had an equal amount of money left. How much money did Ernie hove at first?
Found 2 solutions by ikleyn, SCrappingDude:
Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.
Bertrom and Ernie had $988 altogether. After Bertram spent 4/5 of his money
and Ernie spent 1/3 of his money they had an equal amount o money left.
How much money did Ernie hove at first?
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Write equations as you read the problem

    B + E = 988         (1)     (for the sum of their money, initially)

    %281%2F5%29%2AB = %282%2F3%29%2AE    (2)     (for remaining money)



From equation (2), you have B = %2810%2F3%29%2AE.

Substitute it into equation (1).  You will get

    %2810%2F3%29E + E = 988

    10E + 3E = 3*988

       13E   = 3*988

         E   = %283%2A988%29%2F13 = 228.


ANSWER.  Initially, Ernie had $288;  Bertrom had  $988 - $228 = $760.

Solved.



Answer by SCrappingDude(6) About Me  (Show Source):
You can put this solution on YOUR website!
Let b and e be the amount of money Bertram and Ernie had at first, respectively. We have the system of equations:
b + e = 988
(1/5)b = (2/3)e
Solving for b, we get:
b = 988 - e
Substituting this into the second equation, we get:
(1/5)(988 - e) = (2/3)e
Simplifying, we get:
197.6 - (1/5)e = (2/3)e
Solving for e, we get:
e = 760
Therefore, Ernie had $760 at first.


Here is how to get the answer $760 using Python:

def solve(b, e):
b_left = b * 4 / 5
e_left = e * 2 / 3
if b_left == e_left:
return e
elif b_left > e_left:
return solve(b - b_left, e)
else:
return solve(b, e - e_left)
print(solve(988, 0))

This code outputs the following:
760