Question

a store is having a sale on 200 dvd movies. some of the movies are being sold for $10 and some of them are being sold for $12. if the store made $2200 after selling all 200 dvds, how many $12 dvds were sold?
a 50
b 75
c 100
d 150

Explanation:

Step1: Define variables

Let \( x \) be the number of \$12 DVDs, LXI1 be the number of \$10 DVDs. We know \( x + y = 200 \) (total DVDs) and \( 12x + 10y = 2200 \) (total revenue).

Step2: Express \( y \) from first equation

From \( x + y = 200 \), we get \( y = 200 - x \).

Step3: Substitute into revenue equation

Substitute \( y = 200 - x \) into \( 12x + 10y = 2200 \):
\( 12x + 10(200 - x) = 2200 \)
\( 12x + 2000 - 10x = 2200 \)
\( 2x + 2000 = 2200 \)
\( 2x = 200 \)
\( x = 100 \)? Wait, no—wait, let's check again. Wait, maybe I made a mistake. Wait, let's recalculate:
Wait, \( 12x + 10(200 - x) = 2200 \)
\( 12x + 2000 - 10x = 2200 \)
\( 2x = 200 \)
\( x = 100 \)? But wait, the options have A.50, B.75, C.100, D.150. Wait, maybe I messed up. Wait, no—wait, let's check the total revenue. Wait, if \( x = 100 \), then \( y = 100 \). Then total revenue is \( 12*100 + 10*100 = 1200 + 1000 = 2200 \). Oh, that works. Wait, but the question is "how many \$12 DVDs were sold?" So LXI4, which is option C? Wait, but let me check again. Wait, the problem says "how many \$12 DVDs were sold?" So according to the calculation, it's 100. But wait, maybe I made a mistake. Wait, let's re-express:

Wait, let's do it again. Let \( x \) be \$12 DVDs, LXI1 be \$10 DVDs.
\( x + y = 200 \)
\( 12x + 10y = 2200 \)

From first equation, \( y = 200 - x \). Substitute into second:

\( 12x + 10(200 - x) = 2200 \)
\( 12x + 2000 - 10x = 2200 \)
\( 2x = 200 \)
\( x = 100 \). So the number of \$12 DVDs is 100, which is option C. Wait, but let me check with option A: if \( x = 50 \), then \( y = 150 \). Revenue: \( 12*50 + 10*150 = 600 + 1500 = 2100 \), not 2200. Option B: \( x = 75 \), \( y = 125 \). Revenue: \( 12*75 + 10*125 = 900 + 1250 = 2150 \), not 2200. Option C: \( x = 100 \), \( y = 100 \). Revenue: \( 1200 + 1000 = 2200 \), correct. Option D: \( x = 150 \), \( y = 50 \). Revenue: \( 12*150 + 10*50 = 1800 + 500 = 2300 \), too much. So correct is C.

Answer:

C. 100