76.6k views
3 votes
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 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?

User ThanaDaray
by
7.9k points

2 Answers

4 votes

Answer: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.

Explanation:

I took a test and it was correct also deal with my maths.

User Amirah
by
7.8k points
4 votes

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.


2(1)/(2) 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.


1(1)/(2) 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.



User Orcun
by
7.2k points