Thursday is ladies night at the slurp and burp bar and grill. all adult beverages are $ 1.25 for women and $ 2.50 for men. a tot

The ratio of women to men is 34 to 382. To find the total sales, we compute 382 multiplied by 2.50, resulting in $955. For women, the calculation is 34 multiplied by 1.25, which equals $42.50. Therefore, summing these amounts gives us $955 + $42.50 = $997.50.

Let x denote the number of women and y represent the number of men. We know that the total of 416 adult beverages were sold, which leads us to the equation x + y = 416 (let’s call this equation 1). The beverage prices are $1.25 for women and $2.50 for men, and they totaled $997.50 in sales, giving us the equation 1.25x + 2.50y = 997.50 (let’s refer to this as equation 2). To find x, we will solve these equations. Starting from the first equation, we can express y as 416 - x, and now substituting this expression for y into the second equation, we have 1.25x + 2.50(416 - x) = 997.50. This simplifies to 1.25x + 1040 - 2.50x = 997.50. Rearranging gives us -1.25x + 1040 = 997.50. By isolating x, we find -1.25x = -42.5, resulting in x = 34. Thus, there were 34 adult beverages sold to women.