The drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined 24 regular gift baskets and 7 deluxe gift baskets, earning a total of $839. During the spring musical, they sold 15 regular gift baskets and 8 deluxe gift baskets, earning a total of $673. How much are they charging for the different sized gift baskets?
Let R be the cost of a regular gift basket and D be the cost of a deluxe gift basket.
The drama club sold a combined total of 24 regular and 7 deluxe gift baskets in the fall, so 24R + 7D = $839.
The drama club sold a combined total of 15 regular and 8 deluxe gift baskets in the spring, so 15R + 8D = $673.
We can multiply the first equation by 15 and the second equation by 24 to eliminate R from the equations.
15(24R + 7D) = 15*$839
24(15R + 8D) = 24*$673
360R + 105D = $12585
360R + 192D = $16152
Subtracting the first equation from the second equation gives (192D - 105D) = 12585 - 16152.
Doing the math, we get 87D = 3567.
Thus, the drama club charges D = $<<41=41>>41 for a deluxe gift basket.
Substituting this value into the first equation to solve for R, we get 24R + 7*41 = $839.
24R = 839 - 287
24R = $552
Therefore, the drama club charges R = $<<23=23>>23 for a regular gift basket. Answer: \boxed{23, 41}.