For a card trick, Barry is using 16 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.
16 ÷ 5 + c
B.
16 × 5 + c
C.
16 ÷ (5 + c)
D.
16 × (5 + c)

Answer 1

To find how many suits Barry is using with the cards available, we can analyze the components of the problem.

Barry has 16 cards in total, with each suit containing 5 numbered cards and c face cards. Therefore, each suit has a total of \(5 + c\) cards.

If we let \(s\) be the number of suits, then the total number of cards can be represented by the equation:

\[ s \times (5 + c) = 16 \]

To find the number of suits \(s\), we can rearrange the equation:

\[ s = \frac{16}{5 + c} \]

Now let's compare our derived expression to the options given:

• A. \(16 \div 5 + c\)
• B. \(16 \times 5 + c\)
• C. \(16 \div (5 + c)\)
• D. \(16 \times (5 + c)\)

The correct expression that represents the number of suits being used is:

C. \(16 \div (5 + c)\).