Andy, Bert, and Charles have $20$ pieces of chocolate. Some of the chocolates have nuts, some are plain, and some are filled with caramel (they are split in a ratio of $1:2:2$, respectively). Neither Andy nor Charles can eat nuts, and Charles will always take caramels over plain chocolates if he can (the others are indifferent to plain or caramels). If Andy, Bert, and Charles split the chocolates among themselves in a ratio of $3:1:1$, respectively, in a way that makes each person as happy as possible, how many pieces of chocolate with caramel does Andy receive?

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?