Question

Long-sleeve and short-sleeve T-shirts can be purchased at a concert. A long-sleeve T-shirt costs $25, and a short-sleeve T-shirt costs $15. During a concert, the T-shirt vendor collects $8415 from the sale of 441 T-shirts. How many short-sleeve T-shirts were sold?

a) 336
b) 441
c) 392
d) 504

Answer 1

Through systems of equations, we discover that 261 short-sleeve T-shirts were sold at the concert, which does not match any of the given options. This result suggests there may be an issue with the provided options or the question's premise.

Step-by-step explanation:

To solve for the number of short-sleeve T-shirts sold, let's denote the number of long-sleeve T-shirts as 'L' and the number of short-sleeve T-shirts as 'S'. Given that a long-sleeve T-shirt costs $25 and a short-sleeve T-shirt costs $15, we can form the following equations based on the total sales and the number of T-shirts sold:

25L + 15S = $8415
L + S = 441

We can multiply the second equation by 15 to make the coefficient of S the same in both equations:

15L + 15S = 6615

Now, we subtract this from the first equation:

(25L + 15S) - (15L + 15S) = $8415 - $6615
10L = $1800
L = 180

Now we know that 180 long-sleeve T-shirts were sold. We can use the second equation to solve for S:

180 + S = 441
S = 441 - 180
S = 261

Therefore, the number of short-sleeve T-shirts sold is 261, which is not listed in the provided options, indicating there might be an error with the options or the premise of the question.