Lianna plays a card game in which she gets 5 points for every red card she draws but loses 10 points for every black card she draws. By the end of the game Lianna drew 7 times as many red card as black cards for a final total of 75 points. How many red cards did she drew during the game?
If R = number of red cards B = number of black cards then, 5*R = number of points earned from all red cards -10*B = number of points lost from all black cards 5*R-10*B = total amount of points
This total is equal to 75 points (given) 5*R-10*B = 75
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We are told that "drew 7 times as many red card as black cards" so this means R = 7*B
Use substitution to find that... 5*R-10*B = 75 5*7*B-10*B = 75 ... R is replaced with 7*B 35*B-10*B = 75 25*B = 75 B = 75/25 B = 3
