M47-205

Question

A community theater bought identical costume scarves for a performance. At the supplier’s sale, for every scarf bought at the regular price, the theater bought one additional scarf at half the regular price. How many scarves did the theater buy?

(1) The regular price of each scarf was $18.

(2) The theater spent $216 on the scarves.

Show Answer

Official Answer

C

(1) The regular price of each scarf was $18.
 
(2) The theater spent $216 on the scarves.

Bunuel · Answer

Official Solution:

A community theater bought identical costume scarves for a performance. At the supplier’s sale, for every scarf bought at the regular price, the theater bought one additional scarf at half the regular price. How many scarves did the theater buy? 
 
Let  p  be the regular price of one scarf. Since for every scarf bought at the regular price, one additional scarf was bought at half price, the scarves were bought in pairs. Each pair cost:
 
 p + \frac{p}{2} = 1.5p 
 
(1) The regular price of each scarf was $18.
 
This tells us the cost of one pair:
 
 18 + 9 = 27 
 
But it does not tell us the total amount spent, so we cannot determine how many pairs were bought.
 
Not sufficient.
 
(2) The theater spent $216 on the scarves.
 
This gives the total amount spent, but not the regular price of one scarf, so we cannot determine how many pairs were bought.
 
Not sufficient.
 
(1)+(2) From statement (1), each pair cost:
 
 18 + 9 = 27 
 
From statement (2), the theater spent $216.
 
So the number of pairs was:
 
 \frac{216}{27} = 8 
 
Each pair contains 2 scarves, so the number of scarves bought was:
 
 8 * 2 = 16 
 
Sufficient.
 
Answer: C

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