Question

Type the correct answer in each box. If necessary use / for fraction bars.

Answer 1

Answer: Bill has 12 cards

Alan and Calvin both have 19 cards each.'

Step-by-step explanation:

Let x= Number of cards Bill has.

Then Alan has cards = $2\dfrac{1}{2}x-11=\dfrac{5}{2}x-11$

Calvin has cards = $1\dfrac{1}{2}x+1=\dfrac{3}{2}x+1$

Since Alan and Calvin has equal number of cards.

Then, $\dfrac{5}{2}x-11=\dfrac{3}{2}x+1$

$\Rightarrow\ \dfrac{5}{2}x-\dfrac{3}{2}x=1+11\\\\\Rightarrow\ \dfrac{5-3}{2}x=12\\\\\Rightarrow\ \dfrac{2}{2}x=12\\\\\Rightarrow\ x=12$

So, Bill has 12 cards

Then, Alan has cards = $\dfrac{5}{2}(12)-11=30-11=19$

Calvin has cards = $\dfrac{3}{2}(12)+1=18+1=19$

So, Alan and Calvin both have 19 cards each.