Question

A party store has $54$ packs of plates in stock in either sets of $8$ or of $12$. If there are $496$ total plates in stock, then how many plates would a customer buy, if he buys all of the packs of $12$ that the store has in stock?

• A. $16$
• B. $38$
• C. $192$
• D. $304$

Answer 1

Answer: (C)

$192$

Let the total number of packs of $12$ plates be $x$.

Hence, the total number of packs of $8$ plates will be $54-x$.

Therefore $8(54-x)+12x=496$

$\Rightarrow 432-8x+12x=496$

$\Rightarrow 4x=64$

$\Rightarrow x=16$

Hence, the store has $16$ packs of $12$ plates.

Thus, if a customer buys all the packs of $12$ plates, then he will buy $12\times 16=192$ plates in total.