Question 32812: Peter, Tom, and Vincent have 240 cards altogether. Peter gave some of his cards to Tom and the number of Tom's cards was doubled. Then Tom gave some of his cars to Vincent and the number of Vincent's cards was doubled. If the three boys had the same number of cards in the end, how many cards did Peter have at first?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! P = Peter's cards
t = Tom's cards
v = Vincent's cards
p + t + v = 240
p gives x cards to t
(p - x) + (t + x) + v = 240
we are told that t's cards has now doubled
(a) t + x = 2t
t gives y cards to v
(p - x) + (t + x - y) + (v + y) = 240
we are told that v's cards has now doubled
(b) v + y = 2v
and now their cards are equal
(c) p - x = 80
(d) t + x - y = 80
(e) v + y = 80
there are 6 equations and 5 unknowns, sdo we can solve
(a) t + x = 2t
x = t
(b) v + y = 2v
y = v
(e) v + y = 80
2v = 80
v = 40
y = v
y = 40
(d) t + x - y = 80
t + t - 40 = 80
2t = 120
t = 60
so far v = 40, t = 60
p + t + v = 240
p + 100 = 240
p = 140
Peters cards = 140, Tom's = 60, Vincent's = 40
check:
p + t + v = 240
40 + 60 + 140 = 240
(c) p - x = 80
140 - 60 = 80
(d) t + x - y = 80
60 + 60 - 40 = 80
(e) v + y = 80
40 + 40 = 80
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