For a card trick, Barry is using 28 cards from a deck. If each suit he uses has 5 numbered cards and c face cards, which expression shows how many suits he is using?

Question

A.
28 × (5 + c)
B.
28 ÷ (5 + c)
C.
28 ÷ 5 + c
D.
28 × 5 + c

Answer 1

To find how many suits Barry is using, we need to think about the total number of cards he is using, which is 28, and how many cards are in each suit.

Each suit has:

• 5 numbered cards
• c face cards

So, the total number of cards in one suit is: \[ 5 + c \]

Now, if he is using \( x \) suits, the total number of cards he has in terms of \( x \) would be: \[ x \times (5 + c) \]

Since we know that the total number of cards he is using is 28, we have: \[ x \times (5 + c) = 28 \]

To solve for \( x \), we can rearrange the equation: \[ x = \frac{28}{5 + c} \]

Thus, the expression that shows how many suits he is using is: \[ 28 ÷ (5 + c) \]

So, the correct answer is: B. \( 28 ÷ (5 + c) \).