SOLUTION: Alice had twice as much money as Peter. After Alice spent 1/6 of her money and Peter spent 2/3 of his money, they had a total of $720 left. (a) How much money did Alice and Pete

Question 1188380: Alice had twice as much money as Peter. After Alice spent 1/6 of her money
and Peter spent
2/3 of his money, they had a total of $720 left.
(a) How much money did Alice and Peter have altogether at first?
(b) Peter spent 3/4 of his remaining money on a bag. What fraction of his
original amount of money did he spend on the bag?
(Give your answer in its simplest form.)

Answer by ikleyn(52767) (Show Source): You can put this solution on YOUR website!
.
Alice had twice as much money as Peter. After Alice spent 1/6 of her money
and Peter spent
2/3 of his money, they had a total of $720 left.
(a) How much money did Alice and Peter have altogether at first?
(b) Peter spent 3/4 of his remaining money on a bag. What fraction of his
original amount of money did he spend on the bag?
(Give your answer in its simplest form.)
~~~~~~~~~~~~~~~~

I will solve part (a) only.

Let x be the amount Peter had at first, in dollars.

Then Alice had 2x dollars.


Write equation for the total remaining money after spending, as you read the problem


    {{(5/6)(2x)}}} +  = 720  dollars.


To solve, multiply both sides of the equation by 6 and simplify


    10x + 2x = 6*720

       12x   = 6*720

         x   =  = 6*60 = 360.


ANSWER.  Peter had $360 at first;  Alice had twice of it, i.e. $720 dollars.

         Altogether, they had 360 + 720 = 1080 dollars, at first.

Solved.

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