phoenix9801 wrote:Question 1
Joseph and Charmaine agree to trade basketball cards. Joseph starts with twice as many basketball cards as Charmaine. He later has only 14 more than she does after he gives her 6 of his cards. What is the total number of cards they started with?
a) 27
b) 30
c) 39
d) 60
e) 78
We can plug in the answers, which represent the total number of cards.
Since Joseph has twice as many cards as Charmaine, for every card that Charmaine has, Joseph has 2 cards, implying that Charmaine has 1 of every 3 cards.
In other words, Charmaine has 1/3 of the total number of cards.
Answer choice C: 39
C = 1/3(39) = 13 and J = 39-13 = 26.
After the exchange of 6 cards, C = 13+6 = 19 and J = 26-6 = 20.
New difference = 20-19 = 1.
Way too small: after the exchange, J must have 14 more cards than Charmaine.
Eliminate A, B and C.
Answer choice E: 78
C = 1/3(39) = 26 and J = 78-26 = 52.
After the exchange of 6 cards, C = 26+6 = 32 and J = 52-6 = 46.
New difference = 46-32 = 14.
Success!
The correct answer is
E.
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