SOLUTION: 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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1209424: 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.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~ 

Let x be the Bob's payment, in dollars.

Then the first Peter payment was  %282%2F3%29x.

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


The sum of the Peter's both payments is

    %282%2F3%29x+%2B+46  dollars.


According to the condition, this sum is %284%2F5%29x.

So, our equation is

    %282%2F3%29x+%2B+46 = %284%2F5%29x.


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.   ANSWER


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

        %284%2F5%29%2A345 = 276 dollars.   ( correct ! )

Solved.



Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


At first Peter paid 2/3 of what Bob paid.

So let 2x and 3x, respectively, be the amounts that Peter and Bob paid originally.

When Peter paid $46 more, he ended up paying 4/5 of what Bob paid.

So Peter paid a total of 2x+$46, which is 4/5 of the 3x that Bob paid:

2x%2B46=%284%2F5%293x
10x%2B230=12x
2x=230
x=115

Originally, Peter paid 2x = $230 and Bob paid 3x = $345. Then Peter paid $46 more, for a total of $230+$46 = $276.

The cost of the present was then $276 + $345 = $621.

ANSWER: $621