SOLUTION: Please help me with this: Luisa and Rachel have some trading cards. The ratio of their cars is 3:1. If Luisa gives 2 cards to Rachel , the ratio will be 2:1. How many cards does Lu

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Please help me with this: Luisa and Rachel have some trading cards. The ratio of their cars is 3:1. If Luisa gives 2 cards to Rachel , the ratio will be 2:1. How many cards does Lu      Log On


   

Question 709021: Please help me with this: Luisa and Rachel have some trading cards. The ratio of their cars is 3:1. If Luisa gives 2 cards to Rachel , the ratio will be 2:1. How many cards does Luisa have? It says 18 as in the answer key but i don't know how to get that. Please respond asap. THANK!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number that Luisa has
Let +b+ = the number that Rachel has
given:
(1) +a%2Fb+=+3%2F1+
(2) +%28+a+-+2+%29+%2F+%28+b+%2B+2+%29+=+2%2F1+
----------------------------
(1) +a+=+3b+
(2) +a+-+2+=+2%2A%28+b+%2B+2+%29+
(2) +a+-+2+=+2b+%2B+4+
(2) +a+=+2b+%2B+6+
Substitute (1) into (2)
(2) +3b+=+2b+%2B+6+
(2) +b+=+6+
and, since
(1) +a+=+3b+
(1) +a+=+3%2A6+
(1) +a+=+18+
Luisa has 18 cards
----------------
check answer:
(2) +%28+18+-+2+%29+%2F+%28+6+%2B+2+%29+=+2%2F1+
(2) +16+%2F+8+=+2+
(2) +2+=+2+
OK