SOLUTION: Your friend says that she has a card trick to show. She has separated a deck of cards so that the deck of cards contain no aces or face cards. She asks you to draw a card and then

Algebra ->  Probability-and-statistics -> SOLUTION: Your friend says that she has a card trick to show. She has separated a deck of cards so that the deck of cards contain no aces or face cards. She asks you to draw a card and then       Log On


   

Question 1013792: Your friend says that she has a card trick to show. She has separated a deck of cards so that the deck of cards contain no aces or face cards. She asks you to draw a card and then tells you to multiply the number on it by 7. Next she tells to add the sum of your number and 40 to the product you found. Last she tells you to divide by the sum of your number and 5. She gurentees she can guess this final quotient. Explain how she is able to do this
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= the number on your card
When you multiply the number on your card by 7 , you get 7x .
The sum of your number and 40 is 40%2Bx .
When you add the sum of your number and 40 to the product you found before, you get
7x%2B%2870%2Bx%29=7x%2B40%2Bx=8x%2B40=8%28x%2B5%29 .
When you divide by the sum of your number and 5,
you are dividing 8%28x%2B5%29 by x%2B5 ,
and you get
8%28x%2B5%29%2F%28x%2B5%29=highlight%288%29 .