Alan, brian, calvin are playing a game with collective cards. At the moment. Alan has 11 less than 2 1/2 times the number of cards bill has. Calvin has 1 more than 1 1/2 times the number of cards bill has. If alan and Calvin have the same number of cards, the number of cards bill has is .. the number of cards alan and calvin each have is ... if alan, bill, and calvin have all the cards in the deck, then the deck has ... cards.
Answers
Answer:
50
Step-by-step explanation:
Let A be the number of cards Alan has
B be the number of cards Bill has
C be the number of cards Calvin has
Alan had 11 less than 2 1/2 times the number of cards bill has.
is 2.5
Alan is 2.5 of bill has minus 11
A=2.5B -11
Calvin has 1 more than 1 1/2 times the number of cards bill has.
is 1.5
Calvin is 1.5 of bill has plus 1
C=1.5B + 1
Alan and Calvin have the same number of cards
So A=C
WE plug in A and C equations and solve for B
2.5B -11 = 1.5B + 1 (subtract 1.5B on both sides)
1B -11 = 1 (Add 11 on both sides)
B = 12
If Alan and Calvin have the same number of cards, the number bill has is 12
The number of cards Alan and Calvin each have is 19
Total cards = 12 + 19 + 19 = 50
If Alan, bill, and Calvin have all the cards in the deck then the deck has 50