Question 1209424
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Hi
The cost of a present was shared between Peter and Bob. 
At first Peter paid 2/3 of what Bob paid. 
When Peter paid $46 more, he ended up paying 4/5 of what Bob paid. 
What was the  cost of the present. 
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Let x be the Bob's payment, in dollars.

Then the first Peter payment was  {{{(2/3)x}}}.

The second Peter's payment was  $46 additional dollars.


The sum of the Peter's both payments is

    {{{(2/3)x + 46}}}  dollars.


According to the condition, this sum is {{{(4/5)x}}}.

So, our equation is

    {{{(2/3)x + 46}}} = {{{(4/5)x}}}.


Now simplify and find x.  To do it, multiply both sides by 3*5 = 15 and continue

    10x + 690 = 12x

    690 = 12x - 10x

    690 = 2x

    x = 690/2 = 345  dollars.


It is the Bob's payment.


First Peter's payment was 2/3 of 345 dollars, i.e. 230 dollars.


After the second Peter's payment, his part becomes  230 + 46 = 276  dollars.


Hence, the total cost of the present is 345 + 276 = 621 dollars.   <U>ANSWER</U>


<U>CHECK</U>.  Check that 276 dollars is 4/5 of 345 dollars:

        {{{(4/5)*345}}} = 276 dollars.   ( correct ! )
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Solved.