SOLUTION: Ali,Ben and charles shared teh cost of a present. The ratio of the amount paid by ali to the total amount paid of Ben adn charles was 2: 3 while Ben's share was 20% o fthe total am

Question 894900: Ali,Ben and charles shared teh cost of a present. The ratio of the amount paid by ali to the total amount paid of Ben adn charles was 2: 3 while Ben's share was 20% o fthe total amount paid by ali and charles. Given that charles paid 84 more then Ben, How much did the present cost.?
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
a+b+c=p
2/3=a/(b+c),
b=.2*(a+c),
c=b+84
a = 126, b = 52.5, c = 136.5, p = 315
The present cost 315

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let the amounts paid by each = a, b, and c
given:
(1)
(2)
(3)
------------------------
This is 3 equations and 3 unknowns, so it's solvable
Multiply both sides of (1) by
(1)
(1)
and
(2)
(2)
(2)
--------------------
Substitute (2) into (1)
(1)
(1)
(1)
(1)
----------------------
Substitute (1) into (3)
(3)
(3)
(3)
(3)
(3)
and
(3)
(3)
(3)
(3)
and
(1)
(1)
(1)
(1)
(1)
and

The present costs $315
------------------------
check:
(2)
(2)
(2)
(2)
OK
Hope I got it!

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