algebra word problem

Question

It costs a band $8 per T-shirt produced. At a small festival the band gives away 10 T-shirts, and sells others for $20 each. Their total T-shirt-related profits (taking into account those they gave away) is $304, how many T-shirts did the band sell?

Answer 1

Let T be the number of T-shirts sold, so 8T is the cost of production.

Total sales is 20(T-10)=20T-200 because 10 shirts were given away for free.

Total profit is $304=20T-200-8T=12T-200; 12T=504, T=42 sold, including the giveaways.

CHECK

10 were given away so only 32 were sold, sales=20×32=$640.

42 were made, costing 8×42=$336.

Profit=640-336=$304.