SOLUTION: Monica spent {{{1/2}}} of her money and another $5 on prawns. She then spent {{{1/2}}} of the remaining money and another $3 on chickens. Finally, she spent {{{1/2}}} of what was

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Monica spent {{{1/2}}} of her money and another $5 on prawns. She then spent {{{1/2}}} of the remaining money and another $3 on chickens. Finally, she spent {{{1/2}}} of what was      Log On


   

Question 1184755: Monica spent 1%2F2 of her money and another $5 on prawns. She then
spent 1%2F2 of the remaining money and another $3 on chickens. Finally,
she spent 1%2F2 of what was left and another $2 on vegetables. She
was left with $1.50 in the end. How much money did she have at
first?
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Monica spent 1%2F2 of her money and another $5 on prawns.
She then spent 1%2F2 of the remaining money and another $3 on chickens.
Finally, she spent 1%2F2 of what was left and another $2 on vegetables.
She was left with $1.50 in the end. How much money did she have at first?
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Solve the problem in a backward manner.

For it, represent Monica spendings by steps.


    (1)  She spent 1%2F2 of her money and another $5 on prawns. 


    (2)  She then spent 1%2F2 of the remaining money and another $3 on chickens. 


    (3)  Finally, she spent 1%2F2 of what was left and another $2 on vegetables. 


    (4)  She was left with $1.50 in the end.



It means that immediately before step (3), she had  (1.50 + 2)*2 = 3.50*2 = 7 dollars.


Hence, immediately before step (2), she had (7 + 3)*2 = 10*2 = 20 dollars.


It means that immediately before step (1), she had  (20+5)*2 = 25*2 = 50 dollars.


So, at first, Monica had 50 dollas.    ANSWER


You can check my answer by moving from the beginning to the end.

Solved.