Alan, bill, and calvin are playing a game with collectible cards. at the moment alan had 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 bill has 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?

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 cards.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: